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A PRACTICAL TREATISE 

ON 

COMPRESSED AIR 

AND 

PNEUMATIC 
MACHINERY 

BY 

EDWARD A. R1X AND A. E. CHODZKO 

PNEUMATIC ENGINEERS 

FOR THE 

X -FULTON 

Engineering ^ Shipbuilding Works 

SAN FRANCISCO 



MANUFACTURERS OF 



MINING, MILLING, SMELTING AND 
ELECTRICAL MACHINERY 

ENGINES, BOILERS, HEATERS, PUMPS, ETC. 



Main Office and Branch Works, 213 First St. 
Main Works, Harbor View 

SAN FRANCISCO, CALIFORNIA 



L9373 

Curves, Tables and Engineering Data in the body 

of this Treatise are original and were 

prepared by 

EDWARD A. R1X AND A. E. CHODZKO 

PNEUMATIC ENGINEERS 

San Francisco, - California 



Entered according- to Act of Congress, in the year 1896, 

by 

THE FULTON ENGINEERING AND SHIPBUILDING WORKS 

AND 

EDWARD A. RIX 

In the Office of the Librarian of Congress, 

at Washington, D. C 




COMPRESSED AIR. 



It is a noteworthy fact that, while compressed air has been 

;wn and been used at a time when dynamic electricity was 
even in its infancy, its properties and possibilities are still, 
he minds of many practical people, an object shrouded with 
confusion and mystery, and considered by them as a convenient 
topic for the scientist's investigation, but altogether too intri- 
cate and obscure to be readily grasped by a man possessed of a 
common and average knowledge of motive machinery. 

This same man, strange to say, will find no apparent mys- 
tery in handling a first-class Compound Condensing Steam 
Engine, whose thorough comprehension, however, involves a 
more imposing array of natural phenomena than does the 
action of an air motor. 

Mention to him this latter machine, and he will tell you at 
once that it is useless; he has a vague recollection that com- 
pressed air will not yield over 15 to 20 per cent of the power 
expended to produce it, while an electric motor utilizes 60 or 
80 per cent of this power, and that is the end of it. 

The fact is, however, without in any way disparaging the 
wonderful strides made by electricity, that, in a great many 
circumstances, a compressed air power transmission will be 
found fully as much, and often more effective than an electrical 
transmission. 

Within a radius of 10 to 20 miles or more, it is not a matter 
of theoretical speculation, but a result of actual facts, extend- 
ing over a period of many years' experience, that compressed 
air can be economically produced, conveyed, and utilized as a 
motive power; and if this power is to be distributed through- 
out a number of buildings or factories, or in the interior of a 
mine, the absolute safety consistent with the use of compressed 
air is an element of superiority to which the electrical trans- 
mission has no possible claim. 

However well insulated thexonductors may be, the vicinity 
of a dynamo is always dangerous, either on the ground of fire 
or of bodily injury. 

In a large power station, manned by a picked staff of attend- 
ants, this danger is small indeed; but the conditions are alto- 
gether different if the motor is under the care of a miner or of 
an ordinary workman. 

Again, the location of an air motor is privileged with a con- 
stantly renewed and wholesome atmosphere, whose tempera- 
ture can be, at will, regulated to suit the local exigencies. 

Accidental circumstances which may occur in the vicinity 
of an electric wire under high potential are generally fraught 
with peril. The only accident to which an air pipe is liable is 



4 COMPRESSED AIR. 

a leak, which will cause a loss of power, but which cau be re- 
paired and approached at no risk whatever. 

But now conies another point. 

Referring more especially to the mines which, in California, 
should represent a large percentage of the users of compressed 
air, an example will well illustrate the comparative merits of 
the two modes of power transmission, especially for mines. 

Take a mine which was equipped some years ago; ample 
water power exists several miles away, but the configuration 
of the ground did not permit of conveying the water to the 
mine; a telodynamic transmission would not have been practi- 
cal, so the owners concluded to put up a first-class steam plant 
for hoisting, pumping, and milling purposes, and also for run- 
ning compressors supplying air to the rock drills, and perhaps 
to one or more underground pumps and fans. 

In the course of time, however, timber has grown scarce in 
the surrounding sections, and now they have to haul their fire- 
wood at the rate of $5.00 or $6.00 a cord; as there is quite an 
amount of power used at the mine, this represents a rather 
burdensome item, so the owners begin to investigate some pos- 
sible way out of it. 

An electrical transmission is forthwith proposed to them, 
with tangential wheels and generators near the waterfall, con- 
ductors readily spanning all the intervening ridges and can- 
yons, and a number of dynamos to replace the steam engines. 

It is a practical, feasible, and satisfactory proposition, but 
there is one black cloud in this bright sky: what shall become 
of the steam engines and boilers.? They have to be torn down, 
of course, to make room for the dynamos. This whole plant 
is still, however, in perfect condition; it has been bought, 
hauled, and erected at great cost, and would bring, at a sale, 
about as much as its equivalent of scrap iron, supposing it 
could be sold at all. The proposed plant will assuredly be 
more economical, but this is a dead loss which it will take some 
time to make up for. 

Here comes the opportunity of the compressed-air man; he 
proposes to put up an air-compressing plant at the water-fall; 
the iron-pipe that carries the air will span ridges and canyons 
as easily, for all practical purposes, as did the wires, but after 
it reaches the mine, the list of new material closes, or nearly 
so; for neither the engines nor the boilers will have to be 
touched. The former will v/ork with air as they did before 
with steam, the boilers being used for heaters or air receivers. 

The compressor that used to work at the mine will not even 
have to be discarded, as it may serve either as a reserve or as a 
pressure transformer; in other words, there will have been an 
addition to the mine's possessions, in the shape of the com- 
pressors at the power-house and of the pipes, but the old plant 
will remain just as it was, and give full value for what it did 
cost; it will simply be necessary to find a new job for the fire- 
men and woodchoppers. 

Another very important point: suppose the power plant at 



COMPRESSED AIR. 5 

the water-fall met with accident, or the conductors to be tem- 
porarily crippled; with the electric plant it means a stoppage of 
the whole mine; with the compressed air proposition it would 
only be necessary to fill the boilers, start up the fires, and run 
by steam again. Here, there is no possible competition between 
the two systems. The advocates for electricity claim a superior 
economy, but a few developments on the production and the 
utilization of compressed air will, it is hoped, prove to the con- 
trary, and we will try to illustrate the laws and properties 
of air and compressed air in a simple manner, and with the 
constant remembrance that practical men want plain facts and 
have no use for mathematical discussions. 

It is a common feature with gaseous substances that heat 
has a tendency to increase their volume, or, as the term goes, 
to expand them. Referring more particularly to atmospheric 
air, it will suffice to recall the classical experiment of the cork 
shutting hermetically a bottle full of air, and blown out, if the 
bottle be dipped in hot water. 

Therefore, if a certain amount of air is confined within a 
closed cylinder, at the outside temperature, and then exposed to 
a source of heat, this air will have a tendency to expand, the 
result of which may be twofold. 

If the cylinder is closed, for instance, by two covers tightly 
bolted on, and if its walls and covers are strong enough to 
resist deformation under this expansive tendency, the volume 
of air will remain constant, and its pressure will increase. 

But if we suppose that one of the covers be removed, and 
replaced by a tight-fitting piston free to move in the cylin- 
der, and loaded with a certain weight, when the air is at the 
outside temperature, the piston will descend in the cylinder 
until it is balanced by the pressure of the confined cushion of 
air. 

If now the cylinder is heated, the piston will start slowly 
upward, and then stop when the expansion wall have ceased; 
in this case, the load of the piston, and consequently the pres- 
sure of the air, have remained the same as before heating, but 
the volume of air has increased. 

Summing up these simple facts, we will say, therefore, that 
the effect of heat upon this mass of air is, in the first cfse, to 
increase its pressure under constant volume; and in the second case, 
to increase its volume under constant pressure. The reverse w 7 ould 
happen in both cases; i. e., if we take the closed cylinder full 
of hot air, and if we allow it to cool down to the outside tem- 
perature, the volume of this air will, of course, remain the 
same, but its pressure will fall gradually, until it becomes the 
same as it was before heating. 

In a similar way, if we allow the cylinder with its piston to 
cool down to the outside temperature, the volume of air con- 
fined under the piston will shrink, and the piston will grad- 
ually drop down to the point where it was before the cylinder 
was heated, the pressure, of course, remaining constant. 

Now, following this line of reasoning, we may conceive 



6 COMPRESSED AIR. 

that, if the temperature arouud the cylinder was made colder 
and colder, the pressure of the constant volume of air of the 
first case would keep dropping, and the volume of the mass of 
air at constant pressure, in the second case, would also keep 
shrinking, until, if such a process was carried on far enough, 
the mass of air which we have been considering would be con- 
densed in volume to nothing, and have no pressure at all. 

A simple calculation shows that such a result would occur 
at the temperature of 461 degrees below o Fahr., or 493 degrees 
below the freezing point of water. 

This temperature, which has been approached, but never 
yet reached by any contrivance at present at our command, is, 
so far, a matter of mental conception, but we may, however, 
conceive its existence. It is called the absolute zero, and plays 
an important part in the study of the properties of gases. 

The absolute zero is, therefore, the temperature at which a mass of 
air would have neither volume nor pressure. 

Passing now to a seemingly different subject, although its 
close connection to the preceding facts will soon appear, a few 
words may be said about the fundamental principle which 
forms the basis of all questions relating to the mechanics of 
gases, the Principle of Equivalence of Heat and Work. 

This principle, formulated in plain language, means that 
whenever work is performed, it develops heat; and conversely, that 
-whenever heat is generated, it can be traneformed into work. 

The scope of this principle is exceedingly broad. 

The elementary conception of work involves two distinct 
elements: a force and a motion, and the measure of the 
amount of work developed by a certain force is the product of 
this force, multiplied by its displacement. 

Thus, if we exert a pull of 1 lb., and if we move 1 foot in 
the direction of this pull, the work that we have developed 
amounts to i-foot pound. 

But, while this definition is true in all cases, work, in nat- 
ural phenomena, can assume a very great variety of forms, 
which, moreover, it is not necessary to enumerate here. 

Our daily experience shows us some applications of this 
principle of equivalence, or correspondence, between heat and 
work. 

That work develops heat, we can see in hammering a cold bar 
of iron, which soon becomes hot; we see it in the result of 
human exertion, in the heating of a shaft journal when the 
work of friction becomes too great; in the sparks showing at 
the contact of a revolving wheel, and of a brake-shoe, or at the 
periphery of a grindstone, etc. 

That heat can be transformed into work has been shown in the 
preceding explanations, when we saw a weighted piston lifted 
by heating the air confined beneath it. ' 

The steam engine is another indirect demonstration ot the 
same fact; when the heat developed in the combustion of coal 
generates steam, which accomplishes some work on the piston 
of an engine. 



COMPRESSKD AIR. 7 

It would be useless to multiply examples of this capital 
principle; suffice it to say, that whenever work is performed, 
there is a production of heat. This will not always be sensible, 
especially if the work is slow and gradual, because the heat is 
lost by radiation, by absorption in surrounding bodies, etc., as 
soon as it is developed. 

This subject of the equivalence between heat and work has 
been exhaustively studied and verified, and it is now accepted 
as a fundamental axiom in mechanics. 

One British Thermal Unit (B. T. U.) of heat, i. e., the quan- 
tity of heat required to raise by 1 degree Fahr. the tempera- 
ture of I lb. of water, corresponds to 77 8-foot lbs. of work. 

In other words, 778-foot lbs. of work applied to a certain 
mass of air, for instance, will develop in it 1 B. T. U. of heat; and 
conversely, an amount of heat of 1 B. T. U. stored up in this 
air can develop 778-foot lbs, of work. 

The number 778, or coefficient of correspondence between 
heat and work, is known as the Joule's Equivalent, from the 
name of the physicist who first set precise rules in this respect. 
Joule had fixed the figure at 772-foot lbs., which was for years 
adopted as correct. Subsequent investigation led to make it 
778, and the most recent developments put it at 779. In this 
treatise it has been taken as 778. 

But it is now expedient to clearly explain how a certain 
mass of air, which has been subjected to work, and which has 
therefore accumulated a certain amount of heat, can conversely 
develop work corresponding to that heat. 

Let us take a cylinder full of air at atmospheric pressure, 
and closed at one end, and then let us insert at the other end a 
piston in this cylinder, and exert an effort upon the piston; 
the air confined within the cylinder will be gradually com- 
pressed, and occupy a smaller volume. At the same time, its 
pressure will have increased, and this compression has absorbed 
a certain amount of work, which will be measured by the mean 
pressure which the piston has had to overcome, multiplied by 
the amount of its displacement. 

The pressure on the piston represents a certain number of 
lbs.; the displacement represents a certain number of feet, 
and their product represents a certain number of foot-lbs., 
which measure the work of compression. 

Suppose now that we release the piston; the air confined in 
the cylinder, and whose pressure was solely owing to the effort 
exerted on this piston, will immediately expand and push it 
back, and if there was no friction between it and the cylinder 
walls, it would resume its former position, when the air-cushion 
would be at atmospheric pressure again. In other words, 
every amount of work spent in compressing the air, would be 
entirely returned by the expansion of this air, or, to any work of 
compression corresponds an equal ivork of expansion, if these efforts 
follow each other instantly. 

Here, we did not make any assumption as to the tempera- 
ture of the confined air, which has been supposed to remain 



8 COMPRESSED AIR. 

stationary. But now let us confine, with a piston, a certain 
amount of free air in a cylinder, and let us fix the piston in 
this position so as to prevent it from backing out; and, then, let 
us apply to the cylinder some source of heat. 

The confined air will have a tendency to expand, and as the 
piston cannot move, the pressure will rise; if then we let the 
piston free, the confined air will push it out in expanding, 
until it resumes the atmospheric pressure, and the outside tem- 
perature, and with the same restriction as regards frictional 
resistances. 

We see that in both instances there has been some expan- 
sive work done, and the force that produced it was supplied in 
the first case by the work of compression, and in the second 
case, by the heating of the air. We see also that in this latter 
instance, the pressure of air in the cylinder depended upon the 
amount of heat supplied to it, or, in other words, upon its tem- 
perature, and so did the expansion work. 

Returning now to the definition of the absolute zero, as 
given, which marks, so to say, the ideal limit of existence of a 
gas so far as volume and pressure are concerned, we can 
readily conceive that I lb. of atmospheric air, at 60 degrees 
Fahr., for instance, is the outcome of 1 lb. of air at the tempera- 
ture of absolute zero, to which a sufficient amount of heat has 
been supplied to raise its temperature by 461 +60=521 degrees 
Fahr., and its pressure to 14.7 lbs. per square inch, above a 
vacuum, wliich is the pressure at the absolute zero. 

This pound of air is confined within the atmosphere, as was 
the mass of air of the last example within a cylinder; but 
should it be allowed to expand against a perfect vacuum, it 
would produce an amount of expansion work corresponding to 
the amount of heat which it had received to become atmos- 
pheric air. 

This capacity of producing expansion work is what is 
termed the Intrinsic energy of this pound of air, and its exist- 
ence is, as we see, intimately connected with the conception of 
the absolute zero. 

The amount of work that measures this intrinsic energy can 
be determined from the law of the equivalence of heat and 
work, since we know that by storing up a certain quantity of 
heat in a mass of air, we give it the property of returning a 
corresponding quantity of work. 

The temperature to which a given amount of heat will raise 
1 lb. of different substances is not the same for all of them. 

The specific heat of a substance is the number of B. T. U. 
that will raise by 1 degree Fahr. the temperature of 1 lb. 
of this substance, the specific heat of water being taken as 
unit. We have seen already that the specific heat of water was 1 ; 
i. e., that it takes 1 B. T. U. to raise by 1 degree Fahrenheit the 
temperature of 1 lb. of water. 

The specific heat of air which we have to use in the subse- 
quent developments is 0.2377. 

In other words, it takes 0.2377 of a B. T. U. to raise by 1 



COMPRESSED AIR. 9 

degree the temperature of 1 lb. of air, that is to say, the 
amount of heat that would raise by 1 degree Fahr. the tem- 
perature of 1 lb. of water, will raise by 1 degree Fahr. the 
temperature of 4.2 lbs. of air. 

The quantity of heat necessary to raise by 521 degrees Fahr. 
the temperature of 1 lb. of air is, therefore: 

0-2377X521=123.8412 B. T. U., 
and the corresponding amount of work is, 

123.8412x778=96,348.52 foot lbs., 
which represents the Intrinsic energy of 1 lb. of air at 60 de 
grees Fahr. 

This, of course, presumes that no heat would be either lost 
or gained, by radiation or otherwise, during the expansion of 
air, and this sort of expansion is called Aiiabatic expansion. 

Now, while any one will readily understand that the expan- 
sion of air can be utilized to do useful work on a piston, it is 
also obvious, for practical reasons, that this expansion cannot 
be carried below atmospheric pressure, since creating a vacuum 
would require additional work. 

Consequently, we cannot expect to avail ourselves of any 
portion of the intrinsic energy stored up in atmospheric air, 
under ordinary circumstances. 

With a steam engine wecan obtain a vacuum, or at least a 
pressure inferior to the atmosphere, by condensing the steam, 
but there is no such thing in the air machine. 

Let us observe, moreover, that the intrinsic energy pos- 
sessed by 1 lb. of air is entirely independent of its pressure, so 
long as its temperature remains the same, the work of expan- 
sion being exclusively controlled by the extreme temperatures 
between which the air expands; so that 1 lb. of air at 100 lbs. 
gauge pressure, and 1 lb. of air at 10 lbs. gauge pressure, and 
both at 60 degrees Fahr., possess the same total intrinsic 
energy as 1 lb. of atmospheric air. 

But there is a vast difference between them at a practical 
standpoint, inasmuch as air at 100 lbs., and even at to lbs., can 
do some useful work by expanding down to atmospheric pres- 
sure; part of their intrinsic energy can, therefore, be utilized to 
do some actual work. 

Taking, for instance, 1 lb. of air at 100 lbs. gauge, and at 60 
degrees Fahr. — if allowed to expand adiabatically to atmos- 
pheric pressure, it will produce work, and consequently lose 
part of its heat, and we find that its temperature, after the 
expansion has taken place, is: — 173.95 degrees Fahr. 

The drop of temperature is: 

173-9^+60=233 95 degrees, 
and as 778x0.2377=184 93, the work of adiabatic expansion is: 
184.93x233-95= 43,264.37 ft. lbs. 

this being the useful work, 

The adiabatic work of expansion from 173. 95 
degrees Fahrenheit to the absolute o would 
be: 18493X287.05= 53,084.15 " " 

Total, 96,348.52 " ' 



COMPRESSED AIR. 




COMPRESSED AIR. II 

which is the total intrinsic energy — that is to say, we have 
utilized 45 per cent of the total intrinsic energy. 

Next, taking air at 10 lbs. gauge, the temperature after adia- 
batic expansion to atmospheric pressure is — 12.9 degrees Fahr. , 
and the useful work of expansion is: 

184.93x72.9= 13,481.39 ft. lbs. 

The adiabatic expansion from — 12.9 degrees 
to absolute zero would give: 

184.93x448.1= 82,867.13 " " 

Total, 96,348.52 " <( 
i. e., the total intrinsic energy, and the useful work is here 14 
per cent of the total intrinsic energy. 

It is hardly necessary to say that these figures are theoreti- 
cal, because, in practise, part of the work of expansion, and 
consequently part of the heat, is absorbed by the friction of 
the piston in the cylinder, and lost by radiation from the vari- 
ous pieces of the machines. 

We see, therefore, that the only portion of the intrinsic 
energy of air that is practically obtainable is the expansion 
work which it does above atmospheric pressure; i. e., that the 
pressure of this air must be raised above the pressure of the 
atmosphere. 

From the preceding developments we might rightly con- 
clude that this result would be reached by heating the air, 
previously confined within a closed vessel, to a proper temper- 
ature. But in practise, such a process would prove unaccept- 
able. 

Compressed air is slow in taking up heat, because its con- 
ductivity is small ; i. e. , because the heat is slow to penetrate the 
whole mass of air, and its low specific heat causes it to cool 
down rapidly. 

Then, again, the whole amount of expansive work above 
atmospheric pressure could not, as said before, be obtained in 
practise; so that raising the pressure of air by mere heating is 
not a practical proposition, and it is necessary, in order to 
meet the requirements of its industrial applications, to operate 
this rise of pressure by direct compression; i. e., by acting upon 
the air, confined in a cylinder, through a piston to which an 
adequate amount of power is applied. 

This compression, in whichever way the rise of pressure 
occurs during its process, is always affected on the following 
general lines: 

A cylinder A (Fig. 1), closed at both ends by covers, con- 
tains a piston B, which can move back and forth therein, and 
whose rod C is connected, either to the piston of a steam 
engine, or, through a connecting-rod and a crank, to a revolv- 
ing shaft. 

Kach one of the cylinder covers carries one or more inlet 
valves a, a f , through which the atmospheric air can penetrate 
into the cylinder; each valve, of course, opening inward, and 
being maintained tightly pressed upon its seat by a spring. 



12 COMPRESSED AIR. 

The covers also carry one or more discharge valves C 67, 
similarly kept closed by a spring, and opening outward into 
closed chambers g, k, connected by a common conduit c, 
which leads to a closed receiver r, whence a pipe attached to 
the nozzle s, conveys the air to the place where it is proposed 
to use it. 

All the valves being closed, and the piston B at one end of 
its stroke, as shown, if it is set in motion from the left to the 
right, a partial and increasing fall of air pressure will occur 
behind it, and soon overcome the tension of the spring which 
keeps the inlet valve a closed; this valve opens, and atmos- 
pheric air rushes into the cylinder, behind the receding piston. 

On the right side of this latter, we have, at the beginning of 
the stroke, a cylinder full of atmospheric, or, as generally 
called, of free air; the inlet valve a, and discharge valve b, are 
both closed, and so remain as the piston moves from left to 
right, because the air pressure in the cylinder has a tendency 
to close the inlet valve a\ whilst its pressure is not sufficient to 
lift the discharge valve b' '. 

The piston continuing to move, the air pressure constantly 
increases, until, at a certain point n, of the stroke it reaches, or 
slightly surpasses, the receiver pressure. 

The action of this latter on the outerside of the discharge 
valve b' , and also the tension of its spring are now balanced, 
and the smallest subsequent move of the piston opens this 
valve, and the compressed air is forced through it into the 
receiver, until the piston reaches the end of its stroke, when 
the discharge valve is closed by its spring. 

An inverse series of operations will occur during the reverse 
stroke, and so on. 

An analysis of these operations shows that during any one 
stroke of the piston there are three distinct classes of work per- 
formed: on one side of the piston, a work of suction; on the 
other side, first a work of compression, under variable piston 
load, and then a work of delivery, under constant piston load. 

This is quite similar, only in the reverse order, to what 
occurs in the cylinder of a steam engine, wherein a certain 
volume of steam is admitted under full pressure, and then, 
after cutting off its ingress, is allowed to expand during the 
remainder of the stroke. 

The work of suction, which overcomes the inertia of the in- 
let valves, the tension of their springs, and the resistance of 
air in its passage through the valve apertures, is always small, 
and can be reduced by properly proportioning and constructing 
the inlet valves. 

It is, therefore, a matter of correct design, which has nothing 
to do in the present developments, and no further mention of 
it will hereafter be made. 

Of the two other qualities of work, the peiiod of delivery 
does not either offer any peculiar feature to investigation 
besides its relative proportion to the whole stroke, inasmuch as 
it is symbolized by a constant load acting against the piston, 



COMPRESSED AIR. 13 

along a certain distance, which corresponds to the elementary 
definition of work as previously given. 

We are thus left to concentrate our attention upon the 
period of compression. 

The variations of volume and of pressure of air, which occur 
gradually during the process of compression, do not follow the 
same law in all cases; that is to say, this variation is different, 
whether the compression takes place at a constant temperature 
(isothermal compression) without any loss or gain of heat, or 
by allowing the increasing heat developed during the com- 
pression to remain integrally in the air; in other words, if the 
compression is done at variable temperature (adiabatic com- 
pression). 

There is no intention to develop here the laws governing 
the pressure and volume of air in those two sorts of compression . 

This would necessarily involve the use of mathematical 
formulae, which we wish to avoid. Suffice it to say that, if the 
temperature of the air remained constant throughout the compression, 
the volume which it occupies at any moment would vary in- 
versely as the pressure. 

Taking, for instance, 1 cubic foot of free air at 60 degrees 
Fahr. , its pressure is, therefore, 1 atmosphere, or 14.7 lbs. per 
square inch above a vacuum, or also zero gauge pressure. 
Suppose that this air is confined under the piston of a 
closed cylinder, and that, driving this piston forward, we 
reduce the volume occupied by the air to }i cubic foot only, at 
the same time maintaining always its temperature at 60 degrees 
Fahr. Then the pressure of this air would be 29.4 lbs. per 
square inch above a vacuum (or 14.7 lbs. gauge), that is, twice 
what it was before. 

If the volume was reduced to )/$ of a cubic foot, its pressure 
would become 3x14.7, or 44.1 lbs. per square inch above a 
vacuum or 29.4 lbs. gauge, always upon the condition that the 
temperature remains, throughout this process, at 60 degrees 
Fahr. 

In other words, if the volume of air becomes 4, 5, 6, 10, 20 
times smaller, its pressure becomes 4, 5, 6, 10, 20 times greater, 
always taking the pressure of the atmosphere (or the gauge pressure 
plus 14 7 lbs. per square inch) as unit, and not the gauge pres- 
sure, which would lead to absurd conclusions. 

These pressures counted above a vacuum are called absolute 
pressures; the pressures indicated by the pressure gauge of a 
boiler are termed effective or gauge pressures. The absolute pres- 
sure is obtained by adding 14.7 lbs. to the corresponding gauge 
pressure; and conversely, the gauge pressure is obtained by 
subtracting 14.7 lbs. from the corresponding absolute pressure. 

Let us take a cylinder open at one end (Fig. 2) and a piston 
moving in it. Suppose that the piston is at 48 inches from the 
cylinder head, that this space has been filled with free air 
through the inlet valve, and that the pipe leading from the 
discharge valve casing communicates with a receiver wherein 
the pressure is 73.5 lbs. gauge per square inch. 



COMPRESSED AIR. 1 5 

We will assume, also, that the compression is isothermal; 
i. e., that the temperature in the interior of the cylinder re- 
mains the same as in the open air. 

If we move the piston 12 inches, the volume occupied by 
the air is 36 inches, or % of its former length, 4^ inches. The 
pressure must, therefore, be the reverse, or % of the atmos- 
pheric pressure; i. e., 19.6 lbs. absolute, or 4.9 lbs. gauge. 

Similarly, when the piston has successively covered 
24, 32, 36, 38.4 46 inches of its stroke, the absolute 

pressures are respectively: 
29.4, 44.1, 58.8, 73.5, 82.2 lbs., and the gauge pressures 
14.7, 29.4, 44.1, 58.8, 73 5 lbs., per square inch, 
which are marked on the sketch. 

If the piston moves further on, as the pressure in the cylin- 
der is the same as in the receiver, the discharge valve opens; 
there is no more compression, and the remaining 8 inches of 
stroke are completed by the piston against a constant gauge 
pressure of 73.5 lbs. per square inch. 

Let us now draw a line, A D, which, at any scale, repre- 
sents 48 inches, and mark on this line some points at 12, 24, 32, 
36, 38.4, and 40 inches from its left end; then draw at those 
points some lines 12-2, 24-3, 32-4, 36-5, 38 4-6, 40-7, perpendic- 
ular to A D. 

Now, on these lines, let us carry, at any other scale, the 
gauge pressure at the corresponding point of the stroke; this 
will give us a succession of points 2-3-4-5-6-7, and, if we join 
them by a continuous line, a curve A B, that represents the 
variations of air pressure during the compression. 

This curve starts from the point A, where the gauge pres- 
sure is zero. 

If we took any number of intermediate points between 40 
and 48 inches of the stroke, the pressure would always be 73.5 
lbs. gauge, and consequently the curve of compression A B is 
followed by a line B C, parallel to A D, and representing the 
delivery under constant pressure: so the diagram A B CD gives 
us a graphic representation of the isothermal compression and 
delivery of air during one stroke of the piston, and its area 
represents the work performed during that stroke, for each 
square inch of piston area. 

The law of isothermal variation of the pressures and vol- 
umes applies to decreasing pressures as well as to increasing 
ones; thus, if we cause one cubic foot of air at 73.5 lbs. gauge 
(88.2 absolute) to occupv 6 cubic feet, its pressure will become 
14.7 lbs. absolute per square inch or o gauge pressure. 

In other words, the curve of isothermal compression is also 
the curve of isothermal expansion, and the diagram A B C D' 
represents either the work of compression and delivery of a 
volume of free air, to 73.5 lbs. gauge, or the expansive work of 
the same body of air at 73.5 lbs, gauge pressure, and expanded 
from that pressure to the atmosphere, when it resumes its prim- 
itive volume. 

The practical meaning of this is, that if we compress a 



1 6 COMPRESSED AIR. 

certain mass of air in a closed cylinder, by pushing the piston 
forward by a certain number of inches, and then, if we let the 
piston free, the air will expand and push it. back; and should 
there be no friction between the cylinder and the piston, this 
latter would return exactly to its starting-point, performing 
during its reverse stroke exactly as much work as has been 
required to push it forward. 

Quite a similar course of reasoning leads us to conclude that 
if we compress air isothermall} 7 in a cylinder, and if its discharge 
valve chamber (this valve being loaded to receive pressure) 
communicates through a pipe of any length, with another 
cylinder exactly alike, located at some distance from the com- 
pressing cylinder, we can obtain isothermally (neglecting 
resistances) from the second cylinder the same amount of 
work that has been developed in the distant first cylinder. 
The first cylinder is the compressor, the second is the motor, 
connected by the air main to the compressor; the whole is a 
perfect compressed air transmission, wherein a given amount of 
work is integrally conveyed to any distance from its point of 
production. 

But were we to establish such a system we would find that 
in practise the work recovered from the motor would not be 
equal to the work developed in the compressor. 

To reduce this difference (which is the keynote of economy 
in this system of power transmission) to be as small as 
possible, constitutes, in a nutshell, the whole scope of pneu- 
matic engineering; and as the first condition to fight a 
difficulty is to locate it, and to size it up, these remarks will be 
concluded by a few explanations showing what are the causes 
of discrepancy between the work expended in the compressor, 
and the work recovered from the motor, and how they can be 
partly eliminated; their total disappearance^ or rather counter- 
acting, being a purely practical matter, which has no absolute 
limitations. 

The fact of compressing air in a cylinder is always accom- 
panied by a production of heat. What causes this heat lo 
develop in the case of air is a question the precise answer to 
which would carry us too far into theory. It may be said 
however, that modern science considers air as formed of 
minute particles in a constant state of vibration, and that com- 
pressing a volume of air which contains a certain number of 
these particles causes them to increase the rapidity of their 
vibratory motions, hence friction, impact, and heat. 

Direct experiment, made from the freezing to the boiling 
point of water, has shown that the pressure of air remaining 
the same, its volume at 32 degrees Fahr. increases by X?3 f° r 
each increase of 1 degree Fahr. in the temperature of this air. 

From this we see that air at the temperature of boiling 
water has increased in volume by l8 % 93 =o.366, or 36.6 per 
cent, whilst this same air, at 493 degrees below -the freezing 
point of water, or 461 degrees below zero Fahr. has shrunken: 
by 49 X9 3 of its volume, or by that volume itself. This is how 
the temperature of absolute zero was ascertained. 



COMPRESSED AIR. 17 

Compression will generate heat, and only should it be pos- 
sible to eliminate it as soon as produced, would isothermal 
compression be obtainable. It might probably be done by a 
very slow and gradual compression, combined with copious 
means of cooling the air in the compressing cylinder. 

But these conditions correspond to a practical impossibility, 
and there is in consequence a considerable amount of heat dis- 
engaged during the compression. The following table gives 
the temperatures Fahr. of dry air at the end of its compression, 
to different gauge pressures iu adiabatic compression; i. e., 
supposing that no portion of the heat developing is lost in the 
course of compression. 



\bsolute Pressure. 


Gauge Pressure. 


Fahr. temperature at 


(Lbs. per sq. in.) 


(I,bs. per sq. in.) 


end of compression. 


14.7 


O 


6o° 


16.17 


1.47 


74-6° 


18.37 


3-67 


94-8° 


22.05 


7-35 


124.9 


25-8r 


11. n 


151-6° 


29.4 


14.7 


175.8 


36.7 


22 


218.3 


44-1 


29.4 


255-1° 


5i-4 


36.7 


287.8 


58.8 


44-1 


3'7 4° 


73-5 


58.8 


369.4° 


88.2 


73-5 


414-5° 


102.9 


88.2 


454-5° 


117.6 


102.9 


490. 6° 


132.3 


117. 6 


523-7° 


147 


132.3 


554° 


220.5 


205.8 


68i° 


294 


279.3 


781 


367.5 


352.8 


864 



We see that as the pressure increases so does the tem- 
perature, and that when, for instance, the pressure has reached 
73.5 lbs. gauge per square inch, the temperature is 414.5 
degrees Fahr., instead of 60 degrees, as was the case in 
isothermal compression. 

The result is, that if we take the same cylinder which was 
used in that case, i. e., if we act on the same weight of free air,, 
this air, when at 73.5 lbs. gauge, will be 354.5 degrees Fahr. 
warmer in adiabatic compression than it would in isothermal 
compression. Its volume must therefore be necessarily greater 
in the former case, since the pressure is supposed to be the same. 

The practical meaning of it is that in adiabatic work the 
period of compression is shorter and the period of delivery is 
longer than in isothermal work; as the work at full pressure is 
naturally greater than at any time during compression, when 
the pressure is smaller, the adiabatic work is greater than the 
isothermal work, to raise the same weight of air to the same 
pressure. 

For 73.5 lbs. gauge, and atmosphere at 60 degrees Fahr., 



l8 COMPRESSED AIR. 

the adiabatic work is 1.31 times the isothermal work. But if 
the work done by the motor is correspondingly greater, what 
harm does the heat do ? There would be none but for the fact 
that the motor is always at some distance from the compressor 
(otherwise there would be no reason to transmit power), and 
the air parting easily with its heat, its passage through the 
receiver and the main will reduce the air to the temperature of 
the atmosphere; i. e., after compressing a volume of hot air 
EC D (7 (Fig. 3), we shall introduce in the motor a volume 
B C D E of cold air of the same weight and pressure. 

Now, this volume will expand in the motor either isother- 
mally or adiabatically. 

As we saw that the work of compression disengages heat, 
similarly, but conversely, does the work of expansion absorb 
heat from the surrounding bodies, and as the isothermal com- 
pression would require a slow process with copious cooling, so 
would the isothermal expansion require a slow process with 
copious heating. Unless this is done, the expansion will be 
rather adiabatic. 

Rather, because if isothermal conditions never strictly 
obtain in practise, the same is true with adiabatic work. 

If we expand adiabatically the volume of air B C D E, at 
60 degrees Fahr. and 73.5 gauge, to atmospheric pressure, the 
work of expansion represented by the diagram B C D K, will 
only be 0.595 of the work of adiabatic compression. 

A compressed air transmission seems, therefore, to be an 
inferior system, the more so as the above figures do not take 
into account all the losses incurred, but only the thermic 
losses; i.e., such as are due to loss of heat. 

Several means are resorted to in order to reduce this loss. 

Suppose that the volume of cold air, B C D E, when it 
arrives at the motor, be reheated at constant pressure (73.5 
lbs. g. ) until it becomes equal to F C D G; then we shall be 
able to develop in the motor by the expansion of this volume 
of hot air the same work that was used to compress it 
adiabatically. 

So if there was no other loss, the motor would utilize 100 per 
cent of the work of compression. Indeed, should the air arriv- 
ing at the motor be reheated to a higher temperature than that 
reached in the compressor, the work recovered would be 
greater than the work expended; and there is no absurdity in 
this statement, for such a result is easily attained at the cost of 
a certain quantity of fuel, which must be taken into account 
and deducted in figuring up the actual efficiency of the motor. 

Reheating the air upon its arrival at the motor is, indeed, 
the bise of the superiority of compressed air as a medium of 
power transmission. 

No corresponding feature exists with electricity to the pos- 
sibility of increasing at any time the intrinsic energy of the 
motive agency in an easy and inexpensive manner. 

There are, however — at least at present — some practical 
limitations to this reheating ; compressed air cannot conve- 



COMPRESSKD AIR. 



19 




20 COMPRESSED AIR. 

niently be admitted into a cylinder at a temperature much above 
350 degrees Fahr. ; while we have seen that in adiabatic com- 
pression, the temperature corresponding to 73.5 lbs. gauge is 
414.5 degrees, and this illustration points out one reason why 
low pressure air is more economical, for power purposes, and also 
the use of compound compression where the rise of adiabatic 
temperature is small in comparison to single stage machines. 

No lubricants of the ordinary description will be fully active 
beyond this temperature: special oils, however, are made 
which are not decomposed belore 500 to 600 Fahr. But it is 
evident that, could the compressor and motor cylinders, pis- 
tons, and packings be made of a substance that would with- 
stand great heat without injury or the usual lubricants, the 
reheating could be carried far enough to compensate for all 
other losses, a feature exclusively characteristic of air; and 
there is no apparent reason why such a substance could not be 
discovered, and it will reward undoubtedly its discoverer in a 
day not far distant. 

Without entering into many particulars, it may be stated 
that when the compression from atmospheric to receiver pres- 
sure is effected in one cylinder, the air is cooled either by sur- 
rounding the walls of the cylinder with a jacket, and providing 
in the heads some hollow chambers, through which a continu- 
ous stream of cold water is rapidly circulated: this is called 
" dry cooling," because no water comes in contact with the 
air, and represents, without exception, the best American 
practise. 

Or else, a spray of finely divided cold water is injected in 
the body of air under compression. 

Here, the contact is direct between air and water, so this 
system is more effective than the dry cooling; and if the jacket 
arrangement is used in connection with the spray, a marked 
improvement occurs in the cooling of air. 

This wet cooling has, however, some practical disadvantages, 
which led to discarding it in this country, while in Europe i, 
is still found in recent high-class compressing plants. 

Another effective means of cooling consists in compounding 
the compressor; i. e.,in effecting the total compression through 
a series of successive cylinders, in each one of which only a 
partial compression is effected, generating little heat, which is 
more easily dealt with; besides, the air in passing from a cylin- 
der to the next one in the series is discharged through a 
cooler, where it resumes the outside temperature. 

For high pressures, compounding is a necessity, and the 
efficiency of the compression is thereby increased. 

The ideal compression is, of course, the isothermal; and its 
efficiency being 1, we have the following relative efficiencies 
for other systems, when air is compressed to 6 atm. effective, 
namely, 

Adiabatic, without cooling 0.744 

Adiabatic, with jackets .80 

Adiabatic with spray 0.85 



COMPRESSED AIR. 21 

Adiabatic compound (2-stage), jacketed, with 

intercooler but no spray 0.863 

3-Stage compound, with intercoolers and with • 

spray 0.955 

The effect of cooling is first to improve the efficiency of the 
compression; i. e., to use less work in producing it; and then, 
at the same time, the amount of heating is proportionally 
reduced. 

A mere mention will be made of the loss incurred by the 
air pressure on its passage through the main connecting the 
compressor and the motor. 

Tables will be found in this book giving the loss of pressure 
through mains of different lengths and sizes, and for different 
velocities of circulation of air. 

In a general way, and especially in a long transmission, 
there is a conflict between the first cost of the plant and its 
efficiency, which both increase with the size of the main. 

In a properly built line, the loss can be made very small, 
and its value will generally be assumed to suit local conve- 
nience, according to whether the first outlay or the cost of power 
is to have more weight in arriving at a decision. 

It is hoped that the preceding remarks will enable any in- 
telligent reader to form a correct idea of the elements to be 
taken into consideration in installing a compressed air plant or 
compressed air transmission, and briefly they may be enu- 
merated: 

1. An economical prime motor. 

2. A compressor, which, while having a high mechanical 
efficiency, has also means for reducing the heat of compression 
to a minimum during and between the periods of compression. 

3. A pipe line involving the least loss by friction consist- 
ent with the finances at command. 

4. Motors, which, beside possessing a high mechanical 
efficiency, have means to expand the air to the atmospheric 
pressure, which must be done by reheating to as great a tem- 
perature as possible, both before and during the expansion of 
the air in the cylinders or upon the motor wheel. 



TABLES FOR THE LOSS OF PRESSURE OF 
AIR IN PIPES. 

In calculating tables for the loss of pressure in pipes, it has 
been found necessary to take a wide departure from the form 
of the tables usually given in catalogues on Compressed Air, 
and whose simplicity unfortunately does not agree with more 
recent experimental results touching upon the subject. 

The formulce from which such tables are generally estab- 
lished are the outcome of experiments made at the Mount 
Cenis Tunnel, and of Stockalper's more recent investigations 
at the St. Gothard Tunnel. 



22 COMPRESSED AIR. 

Similar formulae have been used, with some modifications 
of detail, bj 7 Professor Riedler, who conducted extensive tests 
upon the. compressed air system in Paris, and they are based 
on the assumption that the loss of pressure varies directly as the 
length of the pipe, and inversely as its diameter. 

Professor Unwin took up the subject, availing himself of 
the results formerly obtained, and his investigation of the laws 
governing the motion of air in long pipes does not support the 
above-quoted conclusions. 

Taking, for instance, three pipes, each 5 inches in diameter, 
wherein air enters at a pressure of 70 lbs. gauge, and at a 
velocity of 20 feet per second, if one of these pipes be one mile 
long, the second 2 miles, and the third 5 miles long, the loss 
of pressure according to Unwin 's formula is: 

4.6 lbs. for the i-mile pipe, 

9.4 lbs. for the 2-mile pipe, 

26.3 lbs. for the 5-mile pipe. 

In other words, the lengths being as: 1 - 2 - 5, 

the drop of pressure varies as: 1 - 2.043 - 5-7 2 ! 

and while the discrepancy is unimportant for short lengths, it 

becomes 14.4 per cent at 5 miles, and would be still greater for 

longer pipes. 

As the logical tendency is toward increasing the practical 
length of power transmissions, a saving of a few pounds of 
loss is important; consequently, in working out a compressed 
air transmission, more precise data are needed. To meet this re- 
quirement, the following tables were calculated from Un win's 
formula. 

From the preceding example we notice that the loss of 
pressure increases more rapidly than the ratio of the lengths; 
besides, this loss does not vary inversely as the diameter of the 
pipe. 

Taking a 4-inch pipe, 2000 feet long, into which air at 60 
lbs. gauge enters with a velocity of 15 feet per second, the loss 
at the lower end will be 1.19s lbs.; according to the old rule, 
the loss in an 8-inch pipe of same length, and at the same 
pressure and velocity of air, would be one-half this amount, or 
°>5975 ^s.; yet Unwin's rule makes it 0.52 lbs. 

In the same way the loss in a 12-inch pipe should be 0.398 
lbs., while its actual value is o.j lbs. Here the loss of pres- 
sure decreases more rapidly than the diameter increases. 

And if we accept the theory that recent rules, when ema- 
nating from a reliable source, are the best, we must conclude 
that no satisfactory approximation to exact results can be ob- 
tained with the proportional formulae. 

In the annexed tables, the air pressure at the entrance to 
the main has been assumed to be 70, 80, 90, and 100 lbs. gauge, 
which figures cover the working pressures at which air will 
generally be admitted to the motors. 

The use of the tables involves a few elementary operations, 
which we have clearly defined in several numerical examples, 



COMPRESSED AIR. 23 

selected to suggest a ready method of solving any ordinary 
problems. 

Some little calculation must of necessity be done, inasmuch 
as to construct a series of tables, which would take into consid- 
eration every element which influences all cases of transmission, 
would necessitate too much elaboration, and would not be de- 
sirable in a treatise of this character. 



EXAMPLE 1. 

500 cubic feet of free air is compressed per minute to 80 lbs. gauge, 
and conveyed through a 6% -inch pipe, 2 miles long. What will be the 
air pressure at the lower end of the pipe? 

Referring to Table Fig. 5, which deals with air compressed 
to 80 lbs. gauge, and starting down column 3 (size of pipe in 
inches) we stop at 6-% ins. On the left side (Col. I) we find 
for the ratio of absolute air pressures at lower and upper ends of 
main : 

-j fi — 0.00000003709 v t 3 1 

(z/, is the velocity of air at entrance to main, in feet per second, 
and / is the length of pipe in feet.) 

Following now the horizontal line to the right until it 
meets the vertical column headed 500, we find 36.5 which is the 
value of v t 2 . 

So z/, 2 1=36.5x5280X2=385,440 
and the ratio of air pressures (Col. I) becomes: 



/ 



1 — 0.00000003709X385,440=0.992 



The pressure at entrance to main is 80 lbs. gauge or 94.7 
lbs. absolute; the pressure at the lower end will be: 
94.7X0.992=93.9 lbs. absolute 

14.7 

Or 79.2 lbs. gauge. 
The loss is: 80 — 79.2=0.8 lbs. 



EXAMPLE 2. 

How many cubic feet of free air per minute, compressed to 90 lbs. 
gauge, can be conveyed in a 9-^6 inch pipe^ 5 miles long, the loss of 
pressure to be 3 lbs.? 

The absolute pressure at entrance to main is: 104.7 l° s - 
The absolute pressure at lower end is: 101.7 " 

Their ratio is: — = 0.971 

104.7 

Referring to Table Fig. 6 (90 lbs. gauge) and following Col. 
3 down to 9-^$ inch, we find on the left of this figure (Col. 1) 



24 



COMPRESSKD AIR. 



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28 COMPRESSED AIR. 

that the ratio of absolute pressures at lower and upper eud of 
main is: 

1 f i — 0.00000002075 z\ 2 / 

and as we know that this ratio is equal to 0.971, we may write: 



0.971=1/ I — 0.C00C0002C 75 z/, 



Or, squaring both members of this equation: 

0.9428=1 — 0.00000002075 v x 2 X528oX5 
Or: 0.0005478 v x *=i — 0.9428 

hence: z;, '=104.4 
which we must find in the horizontal column starting from 
9-^ 7/ ; we see that this number is comprised between 84 (2000 
cu. ft.) and 131. 3 (2500 cu. ft.). 

The required number is intermediate between 2000 and 2500 
cu. ft.; it can, with sufficient accuracy, be obtained by interpo- 
lation: 

131. 3 — 84=47.3. Corresponding to a difference of 500 cu. ft. 
of free air (from 2500 to 2000). 

104.4 — 84=20.4, which, by a simple rule of three, corresponds 
to: §QOY.~—2\$, and the required number of cubic feet of free 
air per minute is: 

2215. 



EXAMPLE 3. 

We desire to convey 1000 cu. ft. of free air per minute, com- 
pressed to 70 lbs. gauge, through a pipe 3 miles long, the loss in 
pressure not to exceed 5 lbs. What must be the diameter of the pipe 1 

This diameter could be determined directly, but through 
calculations more intricate than by the tables, which can be 
used in the following manner: 

The pressure at entrance to main is 84.7 lbs. absolute. 

The permissible loss is 5. 

The pressure at the lower end oi main is: 

79.7 lbs. absolute, 
and the percentage of loss is: 

§3=°-94. 

Referring to Table Fig. 4 (70 lbs. gauge) the right value of 
vf 1 is somewhere in the vertical column headed 1000. 

The length is 15840 feet=/. 

We will try some values of z', 3 and apply them to the cor- 
responding ratio of terminal pressures, until the result is 
exactly or approximately 0.94. 

If the result is not exactly 0.94 we will then take the 
nearest larger commercial size of pipe, thus giving less than 
5 lbs. loss through the main. 

To facilitate these approximations we may remark that, 



COMPRESSED AIR. 29 

using the formula of Col. I, we will have an expression of 
this form: 



-V 



1 — o. 0000000 v 



0.94= 

in which the stars represent some numerical value to be dis- 
covered; or, squaring both members of this equation: 
0.0000000 * * * "* z\ 2 /=i — 0.94 2 
=0.1164 
Let us try v t 2 =4^g, corresponding to a 5-in. pipe, we have 
o. 00000004972 X449 X 1 5840 =0.3536 
which result is much too large. 

We see that we have evidently to take a smaller value of 
z', a since / remains constant, while the factor corresponding to 
4972 diminishes with z\ 2 . 

Trying v x 2 =ioo, which corresponds to a 7%-mch pipe, we 

0.0000000299X100X15840=0.0474 
which is below the value o. 1164 which we desire. 

Taking i\ 2= i83, which corresponds to a 6X-i"ch pipe, we 
0.00000003709X183X15840=0.1075. 

This is the nearest value smaller than 0.1164 and will give 
less than 5 lbs. less; and thus we conclude that the required 
diameter of pipe is 6X ins. 

A short use of the tables will render them quite convenient 
to use: 

The above three examples cover the principal question 
liable to arise in ordinary practise, and the few calculations 
involved are more than balanced by the greater correctness of 
the results derived from Unwin's formulae. 

We can use the tables to find the loss of pressure incurred 
in the passage of air through a pipe of a given diameter and 
length, and with a given velocity of ingress. But it is interest- 
ing to know at the same time the corresponding loss of power. 

With this object in view, a Table (Fig. 9) and curves (Fig. 8) 
are here given, showing the ratio of available power at full 
expansion and without reheating at the lower end of the main 
to the available power at full expansion and without reheating 
at its entrance. 

These curves show that the comparative loss of power is 
always smaller than the comparative loss of pressure, and they 
will be found useful in estimating the total loss incurred in a 
given transmission. 

Each curve corresponds to a certain pressure at the entrance 
to the main, these pressures being, as above, 70, 80, 90, and 
100 lbs. gauge. 

This addition to the study of the frictional losses is intended 
to dispel the confusion frequently made between the loss of 
pressure and the loss of power, there being a common tendency 
to consider those two terms as equivalent. 



COMPRESSED AIR. 




COMPRKSSED AIR. 



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32 COMPRESSED ATR. 

For instance, if air enters a pipe at ioo lbs. gauge pressure 
=114.7 absolute, and is discharged at 80 lbs. gauge, or 94,7 lbs. 
absolute, thus showing a reduction of 20 per cent of gauge 
pressure, it is popularly and erroneously estimated that the air 
has lost 20 per cent of its power. The ratio between the abso- 
lute pressures is 9 4 Xi 4.7=^2.5 per cent. 

Referring to the 100 lbs. curve, we note that the ratio of 
pressures 0.825 lies midway between 92 and 94 per cent ratios 
of power; i. e., corresponds to 93 per cent, showing a loss of 
7 per cent only, instead of the so-called loss of 20 per cent of 
power. 

The explanation of this is, that, while the pressure is 
diminished, the volume is proportionately increased, and the 
real loss of power is the work which the air could perform in 
expanding isothermally from the higher pressure to the lower 
pressure, which work has been absorbed by friction. 

An inspection of the curves (Fig. 8) will show that the actual 
pressure at each point on the main becomes a constantly 
decreasing fraction of the initial pressure as the distance of this 
point from the entrance becomes greater, and these variations 
of pressure are figured by a line at 45 degrees on the co-ordi- 
nate axes. For each absolute pressure, the value of the avail- 
able power at full expansion, as compared with the available 
power at entrance, is carried on the corresponding ordinate, 
and by joining the ends of these ordinates, four curves of 
powers have been drawn, each one corresponding to one of the 
above-named initial pressures. Although a limited range of 
initial pressures has been considered, the following general 
deductions are suggested by an inspection of these curves: 

1. So long as the fall of pressure remains below a certain 
value, which, in the cases considered, is about 50 per cent, the 
loss of pressure is more rapid than the loss of power, and the 
ratio of powers is greater than the corresponding ratio of 
pressures. 

2. When the pressure continues to fall beyond this 
value, the loss of power becomes more rapid than the loss of 
pressures, the ratio of powers remaining, however, greater than 
the corresponding ratio of pressure. 

3. When the absolute pressure in the main becomes — in 
the cases considered — from 1 5 to 25 per cent of the initial absolute 
pressure, the ratio of the powers becomes equal to the ratio of 
the pressures. 

4. The pressure continuing to fall, the loss of power 
becomes much more rapid than the loss of pressure, until the 
pressure is equal to the atmosphere, when the available power 
naturally becomes o. and then negative (a case which is not to 
be considered here), and the ratio of powers is smaller than the 
corresponding ratio of pressures. 

The inspection of the curves also shows that the relative 
deficiency of the power, as compared with the corresponding 
pressure, occurs more rapidly with a low initial pressure than 
with a higher one, and incidentally confirms the foregone 



COMPRESSED AIR. 33 

statement, that, for a given initial pressure and velocity at 
entrance, there is a limit of length to each particular size of 
main, beyond which neither pressure nor power would be 
obtainable at its lower end. the whole pressure having been 
absorbed in overcoming the friction, and the air issuing from 
the pipe at atmospheric pressure. 

And as, on the other hand, the velocity of the air varies 
inversely with its pressure at entrance, the desirability of 
high pressure is apparent, either as permitting the use of a 
smaller pipe to convey a given weight of air, or as increasing 
the distance at which a certain power can be obtained with a 
given size of pipe. This statement refers to the conveyance 
of the air, and is, of course, irrespective of the convenience of 
producing a high air pressure. 



LOSS OF PRESSURE IN THE PASSAGE OF 
AIR THROUGH BENDS. 

In addition to the frictional loss incurred in the passage of 
air through a straight pipe, under given conditions of length, 
diameter, and velocity, another cause of resistance is due to the 
changes of direction in the flow of air. 

The bends in a pipe line should be as few as possible, but 
whenever they are absolutely necessary, as, for instance, when 
leaving the surface of the ground to penetrate in a vertical or 
inclined shaft, abrupt bends should be avoided. The 
branching at right angles by means of a T, so frequently found 
in small-sized steam, air, or water pipe, should be absolutely 
discarded. 

Iron pipes of small size can easily be bent to a larger 
radius, and as to larger pipes, special elbows should be used 
instead of the common fittings, whose radius is always small 
as compared with the diameter of the pipe. 

The annexed table shows that when the mean radius of 
curvature is equal to the diameter of the pipe, the loss incurred 
in the air pressure is nearly four times as great as when the 
radius of curvature is equal to five diameters, so that a pipe 
line may be established with all possible care regarding its 
diameter and the velocity of the air, consistent with a small 
frictional loss, and much of the benefit derived therefrom be 
counteracted by the use of one or two short bends. 

With reference to the table, it will be noticed that it 
applies to bends at a right angle. When a smaller or larger 
arc than 90 degrees is used, a sufficient approximation will be 
obtained in figuring the frictional loss in proportion to the 
length of arc of the bend, as compared with an arc of 90 
degrees, and of same radius. 

If possible, from 15 to 20 feet per second should be the 
average entrance velocity given to air in pipes less than 12 
inches in diameter. Above this the velocity may be increased, 
but never to exceed 50 feet per second, for economical use. 



34 



COMPRESSED AIR. 





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COMPRESSED AIR. 35 

THE INFLUENCE OF THE DIFFERENCE OF 
EEVEE ON THE USE OF COMPRESSED AIR. 

The calculations concerning the applications of compressed 
air are generally based upon the standard values of the at- 
mospheric pressure at the sea level; viz., 14.7 lbs. per square 
inch. The fact that a large number of mines are located 
at a considerable altitude makes it necessary to investigate the 
influence of this condition upon the use of compressed air, and 
it will be shown herein that the differences of level are not 
to be overlooked in designing a system for power transmis- 
sion. The weight of one cubic foot of air, at the surface of 
the earth, and at 32 degrees Fahr., and when the barometer 
stands at 30 inches, is 0.0807 lbs. The position of the mercury 
in a barometer is due to the weight of a column of air. whose 
height would be the thickness of the atmospheric layer that 
surrounds the earth, and as one cubic inch of mercury weighs 
0.491 lbs., the weight of a column of mercury 1 inch square 
and 30 inches high is 30X0.491=14.73 lbs. Hence the con- 
clusion that a column of air 1 inch square and of the height of 
the atmosphere weighs 14.7 lbs., and will balance the weight 
of a column of mercury 1 inch square and 30 inches high. 

The immediate consequence of this is that as we rise above 
the level of the sea at a given place, the atmospheric pressure 
per square inch must decrease, since the height of the column 
of atmosphere pressing on the mercury of the barometer 
diminishes, and we can readily calculate that if the whole at- 
mospheric layer were of equal density, that is, if one cubic foot 
of air had the same weight at any altitude, the thickness of 
our atmosphere would be 26,208 feet, or 4 97 miles. 

Such, however, is not the case. The weight of one cubic 
foot of air varies with its pressure and with its temperature, 
which both change with the altitude. 

It is commonly assumed, that at the same latitude, the 
temperature drops by 1 degree Fahr. for every 340 feet of 
height above the sea level; but this could not be taken as any- 
thing like a general rule, since the temperature is affected by 
many local and variable conditions. It suffices, however, to 
show that the density of air changes with the altitude, but as 
the laws of this variation are imperfectly known, and only for 
moderate altitudes, the exact thickness of the atmospheric 
layer that surrounds our planet is a matter of speculation. It 
is generally conceded, however, to be about 45 miles. 

The variations of atmospheric pressure with the altitude 
have been, in the annexed table, calculated from the sea level 
to io,oco feet above it, and for equal steps of 500 feet, on the 
assumption of a constant temperature of 60 degrees Fahr. pre- 
vailing throughout the change of altitude. This supposition, 
however, as we have mentioned before, is not correct, but the 
exact influence of the temperature can easily be computed for 
any particular instance. 



36 COMPRESSED AIR. 

An inspection of the table of atmospheric pressures leads to 
an immediate practical conclusion. Iyet us take, for instance, 
a machine designed to compress at the sea level 500 cubic feet of 
free air per minute to 80 lbs. gauge, that is, 80 lbs. above the 
atmospheric pressure. The volume of cold compressed air de- 
livered per minute is 

500X^=77.6 cu. ft. 
Suppose now that the same compressor be used at 5000 feet 
altitude and run at the same number of revolutions; the piston 
will sweep through 500 cubic feet as before, but the atmos- 
pheric pressure being only 12.14 lbs. per square inch, the 
volume of cold air at 80 lbs. gauge delivered per minute will be 

500X^=65.85 cu. ft. 

That is to say, the delivery of air at 80 lbs. gauge and at 5000 
feet altitude will be 85 per cent of the delivery at 80 lbs. gauge 
and at the sea level, from the same sized compressor running 
at the same number of revolutions. 

These volumetric variations, reckoned upon the volume at 
the sea level taken as a unit, will be found recorded in four 
columns corresponding respectively to 70, 8o, 90, and 100 lbs. 
gauge and annexed to the pressure column. It will be noticed 
that the volumetric efficiency, that is the ratio of the delivery 
at any given altitude to the delivery at the same pressure and 
at the sea level, decreases as the receiver pressure increases. 

We know that in adiabatic compression (which we may 
take as a standard of comparison) the compression to 80 lbs. 
gauge and delivery of 500 cu. ft. of free air per minute absorbs 
79.4 I. H. P. It may easily be calculated that for the same 
outside temperature (60 degrees Fahr.) and the same gauge 
pressure (80 lbs.) the compression and delivery at 5000 feet 
altitude of the same amount of atmospheric air will absorb 
73.7L H. P. 

The ratio of these powers is ^=.928. 
That is to say, we lose in capacity 15 per cent and we gain in 
power 7.2 per cent, which amounts to saying that the produc- 
tion at the same volume of air at the same effective pressure 
will require: 

1 I. H. P. at the sea level, 
1.093 " at 5000 feet, 

1. 1 90 " at 10,000 feet altitude. 

It costs more, therefore, to obtain the same useful work from a 
given compressor at high altitudes than at the sea level. 

Four columns of I. H. P., referring to the compression of 
100 cubic feet of free air per minute to 70, 80, 90, and 100 lbs. 
respectively, are recorded alongside of the volumetric results. 
An inspection of the table shows that if we compare the work 
absorbed by 1 cu. ft. of air delivered at a given pressure, at 
10,000 feet altitude for instance, and at the sea level, the ratio 
will be practically the same within the whole range of pres- 
sures considered. 



COMPRESSED AIR. 



37 



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1 



38 COMPRESSED AIR. 

This is not the only effect of a difference of altitude and 
a practical case will illustrate another side of the question: 

Suppose that a mining plant is located 1500 feet above the 
Compressor plant, and that the Compressor plant itself is 
situated at an altitude of 3000 feet above the sea level, aud 
that the receiver pressure at the compressor is 80 lbs. The 
atmospheric pressure at the elevation of 3000 feet in the Com- 
pressor room is 13. 1 lbs. per square inch. One cubic foot of 
air at the sea level, and at 60 degrees Fahr. weighs 0.0764 lbs. 
One cubic foot of air at 3000 feet elevation and 60 degrees 
Fahr. will weigh 

o.o764Xfj 1 7 =0.0681 lbs. 

Or, 1 lb. of air will represent a volume of 14.68 cubic feet. 
This volume represents a vertical column one inch square and 
2113.92 feet high at the pressure of 13. 1 lbs. per square inch, 
and at a pressure of 80 lbs. gauge or 93.1 lbs. absolute, the 
height of this column weighing 1 lb., and 1 inch square in 
section is 

2113.92X9471=298.06 ft. 

Consequently a column of air at 80 lbs. pressure, 1500 feet 
high, represents a pressure of 5.03 lbs. per square inch. 

The absolute pressure of air, which at the lower end of the 
pipe is 93.1 lbs., is at the upper end: 

93.1 — 5.03=88.07 absolute, 
aud as the atmospheric pressure at 4500 ft. is 12.37 lbs. the ef- 
fective pressure at the hoisting works is 88.07 — r2 -37 l° s -. or 
75.7 lbs. So there is, regardless of the loss due to friction in 
this respect, no loss of volume, but a loss of pressure. 

A very similar course of reasoning would show that when 
compressed air is carried down a shaft the pressure at the 
lower end is greater than the receiver pressure, and this excess 
of pressure, due to the weight of this column of air, will 
generally more than balance any friction al losses there may be 
in the pipes. 

It must be remembered, in this connection, that any motors 
operated by this compressed air will also have a larger back 
pressure to encounter in the exhaust than they would at the 
mouth of the shaft, but still the loss due to this back pressure 
is only a small portion of the gain by the difference of level. 

In both of these examples an exact computation would re- 
quire a consideration of the temperature, but which may be 
neglected in all ordinary propositions. 



AIR ENGINES. 

Compressed Air, like all elastic gases, can be made to oper- 
ate a piston by its expansive force, exactly as does steam, and 
it may be stated in a general way, that any steam engine can 
be actuated by air without altering its arrangement. It is, 



COMPRESSED AIR. 39 

moreover, hardly necessary to add that this statement applies 
to the non-condensing steam engines only. 

Tables are herewith given of the consumption of air per 
minute, reduced to atmospheric pressure, in three classes of 
engines more commonly used; viz: 
The Slide Valve Engine, 

The Automatic Cut-off Engine, Single and Compound, 
The Corliss Engine, Single and Compound. 

Air and Steam, however, while partaking of the same gen- 
eral active property, differ widely in several respects, and a few 
explanatory remarks are here necessary. 

In the first place, the pressure of air may be independent of 
its temperature. This valuable feature, which makes other- 
wise the use of compressed air so convenient, is fraught, how- 
ever, with practical consequences which in many cases, and 
unless provided for, would render it impossible. 

Air, in most cases, expands in a motor adiabatically; i. e., its 
expansion is accompanied by a considerable fall of tempera- 
ture. An additional table is here presented (Fig. 19), giving 
the temperature of exhaust of air, after working expansively in 
the various types of engines considered. This temperature is 
found to range from +7.5 in the slide valve engine to — 143 in 
the Compound Corliss, cutting off at }{ of stroke, the air being 
admitted to the engine at 60 degrees Fahr., and while the for- 
mer temperature might not prove troublesome with dry air, on 
account of the strong exhaust blast of an engine with a late 
cut-off, the latter is decidedly unacceptable, as any lubricant 
introduced in the cylinder would freeze instantly, and the 
exhaust ports be promptly clogged with ice, especially in the 
interior of a mine where the moisture of air is more marked 
than outside. 

It will therefore be necessary for the economical use of air 
to heat it to a certain extent, either before it enters the motor, 
or during the process of its expansion within the cylinder. 
We know already that this operation has also the effect of in- 
creasing the volume of the air at constant pressure. Two 
curves are here presented showing the increase of volume of 1 
cubic foot of air, at 32 degrees Fahr. and at 60 degrees Fahr., 
when heated to various temperatures up to 500 degrees Fahr. 

In connection with this subject of re-heating, another dis- 
tinctive feature of air as compared with steam must be pointed 
out. 

In all non-condensing steam engines, even with an early 
cut-off, the proportions are such as to maintain at the end of 
the period of expansion, a sufficient steam pressure to insure 
a speedy exhaust of the gaseous and of the condensed steam. 
This pressure must of course be greater in a fast moving than 
in a slow engine, with the consequence that part of the energy 
of the steam is thus sacrificed, not uselessly, indeed, but with- 
out doing useful work. 

But with air, there is no condensation during the expansion, 
and also the active gas which operates the piston being the 



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46 COMPRESSED AIR. 

same as the medium into which it is discharged, the exhaust 
pressure may become a very insignificant quantity. 

The result of this is two-fold: First, an air motor, unlike a 
steam engine, can work practically at complete expansion, i. e. , 
the compressed air can expand into the cylinder down to 
atmospheric pressure; and second, this more prolonged ex- 
pansion will be accompanied by a greater fall of temperature. 
So that it may be said that the genuine air motor is inseparable 
from a system of reheating, and also that the complete ex- 
pansion of the air producing a greater variation of load on the 
piston, and of strains on the pieces, an air motor should not 
necessarily but preferably be a compound, rather than a single 
machine. For similar reasons it may rationally be expected 
that turbo-motors of the Parsons' type and DeLaval Rotary 
Engines would be especially well adapted to show a high 
efficiency as air motors. 

It may be inferred, that while an ordinary steam engine will 
perform satisfactory duty if operated with air, a less consump- 
tion of it will be obtained by cutting off earlier in the stroke 
so as to work at complete expansion. This will diminish the 
mean effective pressure throughout the stroke, and, conse- 
quently, the power developed by the engine, at the same time 
extending the range of variation of the strains. 

Such a state of affairs may be acceptable if the load on the 
motor is regular, but if — as will often be the case, especially in 
mining machinery — the load constantl} r varies or else is inter- 
mittent, the air motor at complete expansion must have its 
valve gear so arranged as to permit a later cut-off and, of 
course, a greater or smaller amount of exhaust pressure, which 
amounts to saying that it must be an ordinary steam engine 
susceptible of an earlier cut-off than is commonly used with 
steam. 

Reverting now to the subject of reheating, several systems 
have been suggested and used. 

If the only object was to preclude the obstruction of the 
exhaust ports by the formation of ice due to the moisture of 
air, it would be obtained by the application to this portion of 
the engine, of some source of heat, such as a lamp, or an 
injection of steam, or of hot water. 

This process, however, hardly deserves more than a mere 
mention, for if such a source of heat is handy, it can be used 
to far better advantage in heating the air, either in the cylinder 
or before entering it. 

One method consists in injecting into the cylinder a spray 
of warm water, whose heat is absorbed by the air, while the 
water is cooled. The annexed table gives the weight of water 
at 75 degrees, ioo degrees, and 150 degrees Fahr. to be supplied 
for each pound of air expanding to the atmospheric pressure 
from 70, 80, 90, and 100 lbs. gauge, so that the final tempera- 
ture of air will be 32 degrees Fahr., its initial temperature 
being 60 degrees Fahr. 



COMPRESSED AIR. 



47 



Gauge 
pressure of 


B. T. U. 

required per 
lb. of air. 


Pounds of water per lb. of air, the 
temperature of water being 




75 Fahr. ioo° Fahr. 


350° Fahr. 


lbs. 


(A) 


lbs. 


lbs. 


lbs. 


70 


59- 


i-37 


.86 


• 5 


80 


62.8 


1.46 


.92 


•53 


90 


66.2 


1-54 


•97 


•56 


100 


69.2 


1.61 


1.02 


.6 



Another and better method is to inject steam instead of 
hot water into the C}dinder. The advantages of this system 
are, first that steam, being in a gaseous state, mixes up with air 
more readily than water, even finely pulverized, and besides, 
the condensation of this steam gives up its latent heat, which 
increases considerably the heating of air. 

A comparison of this process with the previous one can 
readily be made. Assuming that a spray of water at 212 de- 
grees Fahr. is injected iuto the cylinder, each pound of this 
water will give up 180 B. T. U. before it is cooled to 32 degrees 
Fahr. 

But, taking steam at atmospheric pressure, i. e., also at 212 
degrees Fahr , 1 lb. of steam, in the process of liquefaction, 
will abandon 966 B. T. U., its latent heat of vaporization, and 
besides 180 B. T. U. as above, making a total of 1146 B. T. U. 

The following table gives the weight of steam at 212 degrees 
Fahr. required for each pound of air to prevent its temperature 
from falling below 32 degrees Fahr. at complete expansion. 

Lbs. of steani at 212 de- 
grees per lb. of air. 

051 

055 



Gauge pressure of air. 
Ivbs. 

70 



B. T. U. required for 
each lb. of air. 

59.0 

.... 62.8 



90 
IOO 



66.2 
69,2 



•059 
.0604 



It is evident that quite similar calculations could be made 
to maintain the exhaust temperature at any given point. Be- 
sides, the use of steam keeps the walls of the cylinder wet, and 
while water alone is a poor lubricant between metallic surfaces, 
it facilitates the action of the regular lubricants, and is also 
favorable to the tightness of the piston packing. 

It will readily be seen that both these methods completely 
preclude the formation of ice in the exhaust ports; their good 
effect is still more pronounced if the cylinder is provided with 
a jacket, into which hot air is circulated. 



4 8 



COMPRESSED AIR. 




COMPRESSED AIR. 49 

Air can also be reheated before being admitted into the 
cylinder. Various designs of heaters are used for this purpose, 
the air generally passing through a system of pipes heated by 
an interior furnace, a flue being provided for the passage of the 
hot gases on the outside of the pipes before they reach the 
chimney. And as air, on account of its bad conductivity, does 
not easily take up heat from the metallic sides of the pipes, it 
is expedient to inject in the pipes a small quantity of water 
which absorbs the heat more readily and penetrates with the 
hot air into the cylinder. 

Another method of heating is to place a lamp or gas jet 
within the air pipe. The use of coal or wood is not advisable 
in this case, as grit and cinders would be carried by the current 
of air into the motor. 

Reheating by the electric current is still in the experimental 
state. 

When the motor is a compound machine, the air should be 
again reheated after it has done work in the H. P. cylinder, 
and before it is admitted to the L. P. cylinder. 

The table giving the temperatures of exhaust in cold air 
work, also gives the temperatures at which air should be 
reheated prior to its admission to the single engines, or to each 
cylinder of the compound engines, in order to exhaust at 32 
degrees Fahr. 

These temperatures are moderate, and can be obtained with 
hot water, or low pressure steam. If the heating is done by 
passing the air through heated pipes, the fuel consumption 
will be very small, as practise shows that 1 lb. of coal gives the 
air from 8,000 to 10,000 B. T. U. in a properly designed 
heater. 

To utilize the full benefit of reheating, and of air expansion in 
compound engines, an early cut-off is very desirable. This 
can be accomplished by reheating to 350 degrees before the air 
enters each cylinder, and Table Fig. 20 shows the amount 
of free air required for various horse powers under this condi- 
tion. A comparision with Table Fig. 16 will show the 
marked advantage of this arrangement. 

Fig. 20^ shows a compound direct connected Corliss 
Hoisting Engine, built by the Fulton Engineering and Ship- 
building Company, in conformity with the data in Fig. 20. 
The air is twice reheated; that is to say before entering the 
high pressure cylinder, and also before entering the low pres- 
sure cylinder. 

For convenience in estimating the power required to com- 
press air and the amount of air which will be furnished by 
given powers, the following tables have been constructed: 

The table in Fig. 21 shows the amount of cubic feet of free 
air at 60 degrees Fahr. and 14.7 lbs. absolute pressure per 
square inch, that can be compressed and delivered per minute 
per I. H. P., adiabatically, in a single stage jacketted cylinder 
compressor, in a two-stage compound jacketted compression 
and in isothermal compression. 



COMPRESSED AIR. 



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COMPRESSKD AIR. 



53 



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COMPRESSED AIR. 55 

This table is constructed from the curve represented in 
Fig. 22. 

In the table the amount of air is given for each indicated 
horse power in the air cylinder and also for each I. H. P. in 
the direct-acting steam cylinder which drives the compressor. 

The table in Fig. 23 is practically the reverse of the pre- 
ceding curve and the table gives the I. H. P. to compress and 
deliver 100 cubic feet per minute of air, at 60 degrees Fahr. and 
14.7 lbs. per square inch absolute pressure. This table is con- 
structed from the curve (Fig. 24) and gives the I. H. P. in the 
adiabatic compression, in single stage jacketed cylinder com- 
pression, in two-stage compound jacketed compression and 
also isothermal compression, and the horse powers under each 
of the different gauge pressures read both for the I. H. P. in 
the air cylinder and the I. H. P. in the direct-acting cylinder. 

Fig. 25 is the curve of mean effective pressures per square 
inch in adiabatic compression, for the various receiver pres- 
sures enumerated. This will be found useful in computing 
piston loads. 

Fig. 26 is a table of pressures per square inch, due to the 
weight of air at 60 degrees Fahr. in vertical pipes, and also the 
weight of one cubic foot of air in pounds avoirdupois. For 
example, if the gauge pressure at the surface of a mine is 70 
lbs. per square inch, at the depth of one thousand feet the 
pressure will be 73 lbs. to the square inch. Where there are 
extreme variations in altitude in a transmission plant this 
weight of air has to be taken into consideration. 



56 



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60 COMPRESSED AIR. 

AMOUNT OF FREE AIR REQUIRED TO RUN 
DIRECT-ACTING STEAM PUMPS. 

In preparing these tables the object has been to furnish 
information to the oft-repeated query, "How many cubic feet 
of free air, compressed to, say 60 lbs., is required to run a 
direct-acting pump that will raise 50 gals, per minute 200 feet 
high, or say 8 miners' inches 150 feet nigh, or at any other 
pressure of air ? " We have made three assumptions in these 
calculations, which are likely to cover all possible losses of 
efficiency in ordinary work. 

First — The work absorbed by the pump has been estimated 
by adding 20 per cent to the actual work in water raised, to 
make up for frictional and other resistances. 

Second — The actual capacity of the air cylinder, that is, the 
volume swept by the piston, has been increased by 15 per cent 
to take into account the clearance, leakage, etc. 

Third — The working pressure of air, when entering the air 
cylinder, has been taken at 10 lbs. per square inch lower than 
the receiver pressure, to compensate for frictional and other 
resistances. 

We have not assumed that the air was reheated before 
entering the cylinder, nor was any account taken of the differ- 
ence of level between the receiver and the pump, which in 
many cases would add several pounds per square inch to the 
working pressure, as noted in the Table (Fig. 26). The 
results given in these tables may therefore be referred direct to 
the intake capacity of the compressor and the estimate of the 
air consumption required is therefore very much simplified. 

If the necessary power to produce the quantities of com- 
pressed air indicated in these tables be compared to the cor- 
responding work in water raised, the efficiency, which is 
measured by the ratio of the latter to the former, will be as 
low as 25 per cent. A direct-acting pump does not use air 
expansively, and this is well known to be a simple but a waste- 
ful manner of transmitting power. 

Assuming the values in these tables to be one, the follow- 
ing table will show the percentages required for the different 
kinds of power-actuated pumps, both for cold air and air 
delivered at 300 degrees Fahr. at the pump motor. 





AIR. 




Cold. (60° F.) 


Reheated to 
300 F. 


Direct Acting Single 


I 
.70 to .60 

.60 
•50 

•33 


.69 

.48 to .41 

.41 

.329 

.226 


Direct Acting Compound 


( Slide Valve Single .... 

Fly Wheel -j Slide Valve Compound 

/ Corliss Compound 



COMPRESSED AIR. 



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COMPRESSED AIR. 63 

REFRIGERATION BY COMPRESSED AIR. 

This Treatise would soon grow beyond reasonable limits if 
it had to enumerate all the applications of compressed air in 
modern industry; in fact, a publication claiming to give an 
exact " up to date'' account of" these applications would never 
come to an end, as some new and unexpected uses are con- 
stantly arising. 

But a review, however cursory, of the properties of com- 
pressed air considered as motive power, must of necessity 
touch upon one of its most interesting uses; viz., the produc- 
tion of cold. A rapid treatment of this question is here the 
more justified as it does not correspond to a class of apparatus 
intended solely for refrigerating purposes. 

Every air motor is in itself, and at no additional cost, a 
cold-producing machine, and this property, which belongs 
exclusively to compressed air, will often be found a valuable 
addition to its other merits, especially by the underground 
worker. 

A quotation from Prof. A. B. W. Kennedy on the Paris air 
installations may fitly be reproduced here: 

"By using air direct from the main in the motor, or by 
heating it only very slightly, the exhaust air can be, of course, 
so greatly reduced in temperature as to be available for freez- 
ing purposes. 

"In one Paris restaurant, for instance, which I visited, I 
found that the exhaust was carried through a brick flue into 
the beer cellar. In this flue the carafes were set to freeze, 
large molds of block ice were also being made for table use, 
while the air was still cold enough in passing away through 
the beer cellar to render the use of ice for cooling quite un- 
necessary even in the hottest weather. 

"The nominal function of the engine in this case was the 
charging of batteries used in the electric lighting of the 
restaurant. 

"The conjoint use of power and cold is common in Paris, 
the power being in this case generally applied to electric 
lighting. While in any large city, such as Paris, it is no doubt 
a great point that by a compressed air system the handiest 
possible cooling appliances can be brought everywhere within 
reach, in tropical climates this is something rather of necessity 
than of luxury. In such cases we might have the apparent 
paradox of a motor worked essentially for its exhaust; the 
work done would be a bye-product, the cold air would be the 
principal thing. 

" In such a case, if there were no useful work to be done, the 
motor could even be made (as has been suggested to me) to 
pump air back into the main, and thus to virtually halve its 
air consumption." 

From these remarks the conclusion is obvious that ice- 
making, water-cooling, and cold-storage contrivances are of 
easy application whenever air motors are used; and it will be 



64 COMPRESSED AIR. 

readily understood that the exhaust temperature of air may be 
regulated by a variation in the degree of heating. 

An inexpensive and tolerably efficient arrangement consists 
of exhausting the air from the motor at one end of a duct 
made of insulating material, such as two or more parallel 
courses of one-inch boards, paper-coated on the outside, and 
secured one or two inches apart by wooden strips; or, else, in a 
more permanent installation the duct may be a brick flue, 
such as described in the above report. 

In both cases its upper portion can be laid open, and 
arrangements are made at the interior of it for suspending ice 
molds, water pails, etc., which are removed at intervals 
depending upon the exhaust temperature of the motor and its 
activity. 

Provision should be made to rid the exhaust air from all the 
grease or oil which it might carry out of the motor before it is 
admitted into the duct. 

One noteworthy feature about air thus used for cooling 
purposes is its wholesome nature; with its defects, adiabatic 
compression is endowed with this beneficial property that the 
combined heat and pressure thus generated prove too much 
for the endurance of microbes; air thus treated becomes thor- 
oughly sterilized, and can be safely put in contact with 
alimentary substances at no risk of contamination. In fact, 
fruits are wonderfully preserved during transportation by a 
new system wherein the exhaust from the air brake cylinders 
is the vital principle. 

More elaborate ice-making or cold-storage appliances might, 
of course, be devised, and special machinery has been con- 
structed to that effect. 

It is not here intended to treat upon the general subject of 
ice-making machines. This cannot be done in an elementary 
way with any degree of completeness. Referring solely to the 
air machine, it may be stated that it is not the most economical 
for cold production, but in many instances it remains in use 
because of its convenience and safety. 

Air is found everywhere, and in case of leakage is not apt, 
like ammonia or sulphur dioxide, to spoil the provisions sub- 
jected to cooling. 

The developments previously expounded in this treatise 
will facilitate the comprehension of the cold air machine, 
which is principally used on shipboard, for the preservation of 
provisions, and for ice-making. 

Two principal types of machines are commonly used. 

THE BEIvL-COLKMAN MACHINE. 

A revolving shaft d, is operated either by a steam engine S, 
and a crank c, as shown on the line drawing, or by a belt 
transmission. 

This shaft carries two flywheels IV, W, and two opposite 
cranks e, f, actuating by connecting rods and crossheads two 
pistons v, h. 



COMPRESSED AIR. 



65 




66 COMPRESSED AIR. 

The piston h travels in a cylinder g, which, for the sake of 
simplicity, has been shown single-acting. The piston h is 
solid, and the back head of the cylinder carries two automatic 
valves z, K. The valve i, opening inward, is an inlet valve 
admitting the free air into the cylinder, during one stroke of 
the piston h; during the reverse stroke the valve i is closed, 
the air confined in the cylinder is compressed, and escapes 
through the outlet valve K, and the pipe /, into a tubular 
cooler, through which a series of tubes t\ establishes a contin- 
uous circulation of cold water. This water enters the cooler 
through the cover m, and is discharged through the opposite 
end n. 

The air delivered by the compressing cylinder g, passes 
around the tubes t, is cooled to, or nearly to, the outside tem- 
perature, and passes through the pipe o y connected to the 
backhead of another cylinder u. 

This cylinder, which is also shown single-acting, has a 
solid piston v, operated by the crank e; the backhead carries 
two separate and closed chambers, containing one an inlet 
valve p, and the other a discharge valve q; but instead of 
acting automatically, these valves have their motion controlled 
by two adjustable cams revolving within the shaft d, as shown 
on the cut. 

While the compression cylinder g delivers at each stroke 
some compressed air into the cooler, the inlet valve p admits 
into the cylinder q a certain volume of this air, which, as said 
before, has been cooled on its passage around the tubes, but 
the setting of the cam operating the valve p on tHe shaft is so 
arranged as to close this valve long before the piston v is at 
the outer end of its stroke; the volume of air introduced into 
the cylinder u is then left to expand adiabatically, and its 
temperature falls to a point which depends upon the amount of 
expansion, i. e. upon the quantity of air admitted by the 
valve/; besides, this work of expansion helps the motion of 
the machine to some extent. For this reason, the cylinder u is 
called the expansion cylinder. 

When the piston v has reached the end of its stroke, the 
discharge valve q is opened by its cam, and so remains during 
the whole reverse stroke, the piston v driving the cold air 
through the pipe r, to the cold storage rooms. 

It will be readily understood that when the valve p closes 
early on the stroke of the expansion piston v, the pressure in 
the cooler increases, and the exhaust temperature in the cylin- 
der u decreases; when, on the contrary, the closing of the 
valve p is retarded, the pressure in the cooler drops, and the 
exhaust temperature rises. So that, by a proper adjustment of 
the cams, the degree of cooling air can be varied within a large 
range. 

This machine is comparatively cumbersome, if the amount of 
cooling is important. 



COMPRESSED AIR. 67 

THE AIvLEN DENSE-AIR MACHINE. 

To obviate this defect, another class of machines has been 
devised, known as the Aeeen Dense- Air Machine. Its gen- 
eral arrangement being practically the same, no special draw- 
ing of it is given. 

The air penetrating into the compression cylinder has been 
primitively raised to a certain pressure, say 40 lbs.; the com- 
pression carries this pressure to, say 160 lbs.; then the air 
passes through the cooler into the expansion cylinder, wherein 
it again expands from 160 lbs. to 40 lbs. or more, according to 
the temperature at which it is desired to discharge it through a 
pipe like r; but instead of being allowed to diffuse freely into 
the cold storage ducts or chambers, this air is circulated through 
coils of closed pipe, which are finally connected to the inlet 
valve chamber of the compression cylinder, the same air being 
thus used over and over again. 

This machine operates upon a greater weight of air under a 
given volume, and consequently is more effective under this 
volume, than the Bell-Coleman machine. Or else, the Allen 
machine can produce the same cooling effect with smaller 
dimensions than the Bell-Coleman, which is an important fea- 
ture on shipboard. 

It is interesting to form an idea of the practical results 
which can be attained with this sort of machine, to which 
object the following data refers: 

One pound of ice at 32 degrees to be transformed into water 
at 32 degrees, absorbs 142 B. T. U. without variation of temper- 
ature. 

This amount of heat, which disappears, without influencing 
the thermometer's indications, is termed the latent heat of 
fusion of ice. In the same way, if we want to transform 1 lb. 
of water at 32 degrees Fahr., into ice at 32 degrees Fahr., we 
must subtract 142 B. T. U. from that pound of water, without 
changing its temperature, and these 142 B. T. U. are the latent 
heat of solidification of water. These two terms are entirely 
equivalent. 

One ton of 2000 lbs. of ice in the process of melting into 
water at 32 degrees Fahr., will therefore subtract from the sur- 
rounding bodies, air, water, or whatever they may be, 2000x142 
or 284,000 B. T. U., and the resulting effect produced on those 
bodies is measured by 1 ton of ice melting capacity. 

The refrigerating action of a machine or process of any 
kind, producing that same effect, is estimated in the same 
terms, and such a machine is said to have a cooling capacity 
of 1 ton ice melting. 

The annexed Table gives the numbers of negative B. T. U. 
and of lbs. of ice melting capacity, developed in the adiabatic 
expansion of 1 cubic foot of air from 60, 70, 80, 90, and 100 lbs. 
gauge respectively to 14.7 lbs. absolute; these are the calculated 
or theoretical capacities. 

These figures show that there is no advantage in using a 
high air pressure, because the refrigerating capacity does not 



68 



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COMPRESSED AIR. 69 

vary proportionately with the rise of pressure; for instance, if 
this latter passes from 60 to 70 lbs., the pressure increases by 
16 per cent and the cooling capacity by 9 per cent; while if the 
pressure becomes 100 lbs. the increase of pressure is 65 per 
cent and the increase of cooling capacity is 23 per cent. In 
other words, the percentage of pressure having increased 4.1 
times, the percentage of cooling capacity rises only 2.5 times. 

No very complete record of experiments has been published 
showing the practical efficiency of cold air machines, one 
reason being that, for this special object, their use is limited, 
as compared with the ammonia machines. But whenever cold 
air machines are adopted, it is because their efficiency is super- 
seded by other practical reasons. Some accurate tests place it 
at 43 per cent of the theoretical cooling capacity of the air for 
the "Bell-Coleman, and 37 per cent for the Allen Dense-Air 
Engine. 

The former coefficient has been used to establish the column 
of the Table headed " Practical Capacity." 

But while in a large city, where ammonia can be readily ob- 
tained a wholesale ice-making and cold-storage business would 
not be undertaken with a compressed air plant, it is none the 
less certain that in mining camps, or in remote localities, where 
cheap motive power is frequently obtainable, the application of 
air to the production of cold remains one of the most interest- 
ing and profitable adjuncts of this valuable power agency. 



70 



COMPRESSED AIR. 





COMPRKSSKD AIR. 71 

POWER TRANSMISSION BY COMPRESSED 
AIR. 

The use of compressed air for transmitting power for a long 
distance is daily gaining in importance, and this application of 
air, which a few years ago did not receive much consideration, 
outside of actuating rock drills and coal cutters, stands at present 
as one of the most economical and satisfactory systems of power 
transmission. 

No fair-minded and impartial person will contend that in 
every possible case in practise one particular system of power 
transmission can be always preferable to all others. 

The economical solution of industrial problems involves so 
many factors of entirely independent and often contradictory 
nature, that the strictly engineering side of the question may 
be overcome in importance by other conditions which would 
hardly have been thought of at a first glance. 

One fact however, may be stated as general, and that is that 
compressed air is better adapted to underground work than any 
other agency of power transmission. Not only can it be trans- 
ported anywhere, through crooked and narrow passages, either 
wet or dry, and regardless of insulation or losses other than 
leakage at the pipe joints, but its use and handling is totally 
devoid of danger, and after its work is done it becomes the 
most essential element to human life. This can be said of air 
alone, although it has nothing to do with its value as a power 
transmitter. 

The principles of the production of compressed air are ex- 
pounded in another part of this Treatise; it is therefore unnec- 
essary to explain here, how, when air has been raised to a 
certain pressure, with production of heat, and when on its pas- 
sage through a long pipe, this air has cooled down to the tem- 
perature of the atmosphere, the loss of efficiency incurred in 
this drop of temperature can be balanced, and even exceeded, 
by reheating the air before it is admitted to the motors. 

This reheating, which can be done at a small expenditure of 
fuel, is an important element in the total efficiency of the 
system. 

Being now in possession of all the essential elements of 
information required in estimating the size and the cost of a 
compressed air transmission, their application to some practi- 
cal examples will form a fitting conclusion to the preceding 
developments: 

EXAMPLE 1. 

A stamp mill is located at 3000 feet from a water wheel 
developing 70 B. H. P. 

Required a compressed air transmission to deliver 40 H. P. 
on the line shaft. 

The motor operating the mill is 500 feet higher up than the 
air receiver, wherein the air pressure is to be 80 lbs. 



72 COMPRESSED AIR. 

Altitude of compressor: 3500 feet above sea level. 
Temperature at compressor and Mill, 50 degrees Fahr. 

The loss from belt-slipping between the cam shaft and the 
motor shaft, and from other causes, can be taken as 10 per 
cent, and the I. H. P. of the motor will be: 

40 

7t=44-4 
and assuming another loss of 8 per cent for clearance, wire 
drawing, etc., the available power at the lower end of the main 
must be: 48.3 H. P. 

As there is, at first glance, an important margin between 
the powers at the wheel and at the mill, it naturally occurs to 
consider whether the reheating of the air at the motor cannot 
be dispensed with. 

We will use a slide-valve engine, cutting off at Yz stroke, 
which would likely be the earliest admissible cut-off as regards 
exhaust temperature. 

The amount of air necessary to develop 48.3 H. P. is: 1.13 
lbs. per second, or 67.8 lbs. per minute. If we were at the sea 
level, 1 lb. of air at 60 degrees Fahr. would represent 13. 1 
cubic feet. 

Sixty-seven and eight- tenths pounds represent, therefore: 
67.8x13.1=888.2 cubic feet. 

If we use a single stage compressor, the I. H. P. required 
for 80 lbs. gauge receiver pressure will be: 
15.18x8.882=134.83. 

But the Table of columns and powers at various altitudes 
shows that the power required to compress and deliver the 
same volume of air at the same pressure, but at 3500 feet alti- 
tude, is (Cols. 5 and 6): 

89xl572 =i.o67 times greater than at the sea level. 
And as the temperature is 50 degrees Fahr., this figure should 
be reduced in the ratio of the absolute temperature (at 60 
degrees and 50 degrees Fahr.) and becomes 1.046. 

The power actually required will therefore be: 

134.83X1.046=141 I.-H. P. in the compressor. 
And if we allow it mechanical efficiency, the brake power on 
the wheel is: 

£=155 B. H. P. 
Whilst we have only 70 B. H. P. at our disposal. 

The air cannot therefore be used cold in the motor; in other 
words, we have not yet a sufficient margin of power between 
the wheel and the mill to permit the use of cold air; reheating 
must necessarily be resorted to. 

We have 70 B. H. P. on the compressor shaft, and 70X0.9= 
63 I. H. P. in the air cylinder. 

From the above calculations, we know that the compression 
and delivery of 100 cubic feet of free air per minute at 80 lbs. 
receiver pressure, and at the given altitude and temperature, 
require: 15.18x1.046=15.88 I. H. P. 



COMPRESSED AIR. 73 

The available power of 63 I. H. P. will permit of compress- 
ing iooXj5g§-=397 cubic feet of free air per minute, whose weight 
at 3500 feet altitude and 50 degrees Fahr. is: 

397X.o8o7X54i--=3o.97- 
Giving per second a weight of air of: 

30.97 c ,, 

-^-=.516 lbs. 

We have next to determine the air pressure at the lower end 
or outlet of the main, for a length of 3000 feet. 

The tables of frictional resistance show that 80 lbs. gauge 
(94.7 lbs. absolute) being the pressure at entrance to the main, 
the pressure at the lower end is: 

With a 4-inch main: 77.7 lbs. gauge. 

With a 3-inch main: 73. lbs. gauge. 

Besides, as the outlet of the main is 500 feet above the re- 
ceiver, we lose from this fact 1.7 lbs., which leaves as available 
pressures at the outlet: 

With a 4-inch main: 76 lbs. gauge. 

With a 3-iuch main: 71.3 lbs. gauge. 

We will use the 4-inch main, and as the necessary reheating 
obviates the low temperature of exhaust caused by a long 
expansion, we will use a motor expanding from 76 lbs. to 2 
lbs. gauge, and find that to develop 48.3 H. P. with 516 lbs. 
of air per second, this air must be reheated to 247 degrees Fahr. 

What amount of fuel this reheating will require can be 
easily computed. 

We have to reheat 30.97 lbs. of air per minute, from 50 
degrees to 247 degrees Fahr., or 197 degrees Fahr. 

The specific heat of air being .238, this will require: 

30.97 X- 238x197=1451.9 B. T. U. per minute, or: 

1451.9X1440=2.090736 B. T. U. per 24 hours. 

And allowing that 1 lb. of coal will yield 10,000 B. T. U. 
209 1 lbs. of coal per 24 hours. 

Or if 1 lb. of pine wood will yield 5400 B. T. U., the weight 
consumed per 24 hours is: 309. ix -5-^5=386.84. 

Or about X cord. 

SIZE OF COMPRESSOR. 

We found as the "useful" amount of air per minute 397 
cubic feet, and allowing .85 volumetric efficency for the com- 
pressor, its intake capacity must be 467 cubic feet. 

With 300 feet per minute piston velocity, and referring to 
Table (Fig. 37), the compressor will be a single 18^-inch ma- 
chine, or a duplex 12^ -inch machine. 

EFFICIENCY OF THE TRANSMISSION. 

The apparent efficiency of the transmission is: 

40 

to 57 
But its exact value should take into account the coal con- 
sumed in reheating the air. 



74 COMPRESSED AIR. 

This latter amounts to 8.70 lbs. per hour, and if we assume 
that in a compound steam engine the coal consumption is 2 lbs. 
per I. H. P., this quantity represents: -^- =4.35 I. H. P. on the 
piston of a direct-acting steam engine operating the compressor, 
or, in the present case, on the compressor shaft. 

The true efficiency is therefore: 

40 

fi5S=-54 
With reverse conditions, i. e., mill 500 feet below compressor, 
the total efficiency would be 55. 

This is an example of a comparatively low efficiency in 
transmission. The power is so small that comparative losses 
become large. This transmission, however, can be improved 
by using a 2-stage compound compressor and motor, the calcu- 
lations for which would be as follows: 

379 cu. ft. of free air at sea level, and 50 Fahr. 4" pipe. 

Absolute pressure I A J entrance 114. 7 lbs. (100 g.) 
y \ At exit, 114 lbs. (99.3 g.) 

COMPOUND MOTOR. 

First reheating, 50 to 350 Fahr. 

Power in H. P. cylinder 32.84 

Second, 153 to 350 Fahr. 

Power in L. P. cylinder 27.26 

Total 60. 10 

First loss, 8 per cent, as in preceding example. 

6o.ix-9 2 =55-29 
Second loss, 10 per cent 

55-29X. 9 =49.76 

on line shaft. 
Coal used for reheating: 12.58 lbs. per hour, corresponding 
to: 6.29 I. H. P. 

Total efficiency: ^^= 652 

65.2 per cent. 

EXAMPLE 2. 

A system of Power Transmission will now be considered in 
the case of a large mine, requiring: 
100 B. H. P. for hoisting ] 

100 ?• 5' £' J° r P U f mpiUg -,i i At the surface. 
100 B. H. P. for a stamp mill { 

25 B. H. P. for lighting J 

And 

25 B. H. P. for hoisting ~] 

25 B. H. P. for pumping j 

1500 cu. ft. of free air per [- At 1500 ft. level. 

minute at 60 degrees Fahr. | 

for rock drills J 



COMPRESSED AIR. 75 

Length of Transmission to surface plant: 4 miles. 
Compressors of the 2-stage Compound type. 
Receiver pressure 75 lbs. gauge. 
Outside temperature 60 degrees Fahr. 
Permissible loss of pressure: 

In surface main: 1 lb. 

In underground: ^ lb. 
Required: 

Size of surface and underground mains. 
Size of Compressor. 
B. H. P. on compressor shaft. 



The power received at the mine will be divided under two 
heads, viz: Surface and Underground. 

SURFACE PEANT. 

We will assume for the motors a mechanical efficiency of .9, 
giving -^=361 H. P.; and then, another loss of 5 per cent 
between the cylinder and the lower end of the main, for wire- 
drawing, elbows, etc. 

The available power at the end of main is: 

361 

^5=380, 

the total efficiency being ^X-Oo^-Sss. 

The absolute pressure at upper end of main is: 89.7 
The absolute pressure at lower end of main is: 88.7 
and the weight of air at this pressure, reheated to 400 degrees 
Fahr. and completely expanded is: 3.26 lbs. per second. 

UNDERGROUND PEANT. 

Pressure at top of main: 88.7 

Pressure at bottom of main 88. 2 

Additional pressure at bottom of main, 4.8, due to weight 
of air. 

Absolute pressure at 1500 level 93.0 

Fifty B. H. P. with .855 efficiency give: 5S.5 H. P., which 
require a weight of air per second of: .59 lbs. 

The rock drills work practically at full pressure, and the 
expansion of 19 lbs. (to 60 lbs. gauge) cannot be utilized. 

The temperature of the compressed air at the bottom of 
shaft column is 250 degrees, and assuming a loss of ico degrees 
before reaching the drills, i. e., a temperature of 150 degrees at 
the drills, the 1500 cubic feet of air will have to be reduced in the 
ratio of: ~, and become: 1275 cu. ft, whose weight is (per 
minute] 97.41 lbs. 

The "total weight of air to be supplied per second is, there- 
fore: 

Surface: 3.26 

Underground: .^,9 
Rock Drills: 1.62 

Total 5.47 lbs. 



76 COMPRESSED AIR. 

corresponding to 4299.43 cubic feet per minute of free air at 60 
degrees Fahr., whose compression, in a 2-stage Compound 
Compressor, will require: 

578.8 I. H. P. 
With .9 mechanical efficiency, the B. H. P. is: 

643 B. H. P. 
The reheating will require 159.34 lbs. of coal per hour, cor- 
responding to: 67 B. H. P., making a total B. H. P. of, 710 
B. H. P. 

The power obtainable at the lower end of main is: 
637.3 H. P. 
and on the shaft of the motors, with .855 efficiency: 
545 B. H. P. 
The total actual efficiency is, therefore: —=76.7. 

SIZE OF MAINS. 

The Tables of frictional resistances, of which the use has 
been explained, give, as proper size of the pipes: 
For the surface main: 12^ inches. 
For the shaft column: 6% inches. 

SIZE OF COMPRESSOR. 

The useful capacity has been found as: 

4299.42 cubic feet of free air per minute. 

Taking for the compressor 85 per cent volumetric efficiency, 
the actual capacity is: 5058 cubic feet, and with 400 feet of 
piston velocity, we will find by referring to Fig. 37 the proper 
size of the compressor. 

It is desirable, for reasons of practical convenience, to 
divide the compressing plant in two equal units, each formed 
of a duplex compound machine. There will be, consequently, 
4 intake cylinders, each having a capacity of 1264 cubic feet per 
minute, which correspond to a diameter of 24^ inches. 

For 75 lbs. gauge receiver pressure, the area of the H. P. 
cylinder should be: 189.36 square inches, corresponding to 15^ 
inch bore, and at the rate of 80 revolutions per minute, the 
stroke will be 2 feet, 6 inches. So the size of cylinders is: 
24 / ^"+i5^"X30 // . 

EXAMPLE 3. 

IOO H. P. DELIVERED BY WHEEL, 2 MILES, 5-INCH PIPE. 

Required: Potential at lower end of line. 
80 lbs. gauge receiver pressure. 

One hundred B. H. P. will compress and deliver 598 cubic 
feet of free air per minute, or 9.95 cubic feet of free air per 
second, corresponding to: 1.546 cubic feet per second of cold 
air at 80 lbs. gauge. 

The velocity at entrance in a 5-inch pipe is: 11.35 feet per 
second, and the absolute pressure at the lower end of the line 
is 94.7X-977=92.52 absolute=77.82 gauge. 



COMPRESSED AIR. 77 

Available work: 

If air is used cold 54.6 per cent. 

If air is reheated from 

6o° to 300 Fahr 79.7 per cent. 

If air is reheated from 

6o° to 350 Fahr 84.9 per cent. 

FUEL CONSUMPTION 

Reheating to 300 Fahr . . .% cord of wood in 24 hours. 
Reheating to 350 Fahr. . . . y 2 cord of wood in 24 hours. 

The total efficiency, taking into account the fuel consumed, 
is, plain expansion, single cylinder: 

Cold Air 546 per cent. 

Reheating to 300 75.9 per cent. 

Reheating to 350 79 per cent. 

The total efficiency, taking into account the fuel consumed, 
using compound cylinders and reheating for both high and 
low pressure cylinders is: 

Reheating to 300 80.7 per cent. 

Reheating to 350 83.3 per cent. 

EXAMPLE 4. 

PUMPING 8 MINER'S INCHES OE WATER 500 FEET HIGH 
WITH DIRECT-ACTING PUMP. 

Consumption of cold free air per minute 352 cu. ft. 

If air is heated (dry) from 6o° Fahr. to 300 Fahr. 
the consumption falls to 241 cu. ft. 

FUEL consumption: 

241 cu. ft.=i8 412 lbs. air per minute. 
1 lb. of air raised in tempera- 
ture by 240 absorbs 57-12 B. T. U. per minute. 

3,427.2 B. T. U. per hour. 

82,252. B. T. U. per 24 hours. 

and 18.412 lbs. will require. ..1,513,452. B. T. U. per 24 hours. 

Assuming 1 lb. wood to yield 5000 B. T. U., and 1 cord= 

2000 lbs. the consumption is: .153 or Ye cord per 24 hours. 



78 COMPRESSED AIR. 



AN EXAMPLE OF A COMPRESSED AIR AND AN 
ELECTRICAL TRANSMISSION. 

To be supplied at the mine: 

ioo H. P. to drive motors and 

500 cu. ft. free air per minute, compressed to 80 lbs. 
The latter requires 83.5. B. II. P. Now, assuming a motor 
efficiency of .95 there will be required at motor in the electrical 
transmission: 

^8 7 .8H.P 87,8 

100 H. P. for machinery. 

~ at motor driving machinery 105.2 

Power at lower end of conductor 193-° 

2 per cent loss on line. 

Power at upper end of line: -7^= *97 

•95 generator efficiency B. 

H. P. on generator: ^ 

207 

AIR TRANSMISSION. 

500 cu. ft. for drills. 
675 for 100 B. H. P. 

1175 
requiring: 11.75X16,7=196.226 H. P. 






RIX AIR COMPRESSORS 



MANUFACTURED BY THE 

Fulton Engineering and Shipbuilding Works 

SAN FRANCISCO, CAL. 



RIX AIR COMPRESSORS 

MANUFACTURED BY THE 

Fulton Engineering and Shipbuilding Works 

SAN FRANCISCO, CAL. 



After the preceding article on the different phenomena and 
laws, both theoretical and practical, which enter into the sub- 
ject of compressed air engineering, it seems right and proper 
to set forth as plainly as possible the different styles and gen- 
eral specifications of the air compressors manufactured espe- 
cially on this Pacific Coast. 

These compressors are all designed and built under the 
special superintendence of Mr. Edward A. Rix, by the Fulton 
Engineering and Shipbuilding Works, and are the result of 
some eighteen years' experience in pneumatics on the Pacific 
Coast. 

There is no doubt that from the conditions under which 
mining is carried on on the Pacific Coast, one would naturally 
expect to see a different style and class of air compressor built 
from those manufactured in the East. The facilities for trans- 
portation are vastly different. The special requirement for 
prospecting plants, which shall be cheap and easily operated, 
and the tremendous heads of water which are found on the 
Pacific Coast, necessitate a peculiar construction of compressor, 
and the large varieties manufactured, descriptions of which 
follow hereafter, give the intending purchaser or operator 
ample opportunity to select machines especially fitted to his 
character of work. 

All of the Rix Compressors are of the water-jacket type; 
that is, the partial cooling during compression is effected by 
circulating water in a jacket around the cylinder and through- 
out the heads of the air cylinder. Frequently, also, this cir- 
culation is carried within the pistons of the machine, but no 
water whatever is injected into the cylinder. This method of 
construction has been constantly followed ever since the manu- 
facture of these machines was begun some eighteen years ago, 
even though during this time the principal Eastern manufac- 
turers were still enamored of the injection system. 

This jacket circulation is not a simple one, and in the small- 
est of the machines is double, that is, there are two independent 
water circulations for the machine, the water entering the 
lower part of the cylinder at two openings, going thence im- 
mediately and independently to each head and then around 



82 RIX AIR COMPRESSORS. 

the body of the cylinder and finally escaping at two inde- 
pendent outlets. 

In all cylinders of large diameter or for high pressure, the 
heads are often built with independent circulations. In this 
manner cold water is assured to many parts of the cylinder at 
the same time. 

All of the Standard Rix Compressors for ordinary use have 
inlet valves of the poppet type, that is, the valves have neither 
nuts nor bolts nor threads, and there is nothing about them to 
get out of order, and they cannot fall into the cylinder. They 
are subjected, of course, to the usual wear and tear in their 
springs, and these may be taken out in a few seconds and re- 
placed as easily. 

The outlet valves of the standard machines are of the check 
valve type, well known to most all builders of compressed air 
machinery. 

The frames are made in two general styles, one of the Cor- 
liss pattern, and the other of fiat bed pattern with slipper cross 
head, one being designed for heavy and one for light duty. 

All of the working parts, such as cranks, boxes, shafts, pis- 
tons, etc., are made in conformity with the best engineering 
practise. The crank pins specially are made unusually large, 
so that they do not heat with the intermittent work which is 
placed upon them. 

The water jackets can be readily cleared out of any mud or 
sediment which may form therein, inasmuch as when the heads 
are taken off the jackets are completely exposed. This is a 
very convenient device. 

Sight feed lubricators and all necessary oilers and standard 
fittings are furnished with every machine. 

In the tables for the various compressors there have been 
no capacities mentioned for cubic feet of free air. Inas- 
much as the cubic feet of free air will depend entirely upon 
the piston speed of the machine and inasmuch as the piston 
speed of the machine depends to a great extent upon a number 
of circumstances, it is deemed easier to use the following table 
to determine the capacities of any of the compressors. It will 
be noted that the left-hand column contains the cylinder 
diameters of the various sized compressors manufactured by 
the Fulton Engineering Company, and on the right of this 
column, under the piston speeds mentioned, will be found the 
various capacities for these cylinders, at the piston speeds 
directly above. 

From this table it will be easy to select the proper size of 
compressor to do the work required, for all the tables in this 
treatise give the number of cubic feet of air required to do the 
various kinds of work. It will only be necessary then to find 
the total number of cubic feet required and to select the piston 
speed most advantageous to at once determine the proper size 
of cylinder. For example, from the requirements if it has been 
determined that 350 feet of piston velocity per minute is as 
much as is desirable and that the cubic feet of air required is 



R1X AIR COMPRESSORS. 83 

about 550 cubic feet per minute, then an 18 54 -inch cylinder 
would be the proper size for a single compressor, or a duplex 
14^, making somewhat less than 300 feet of piston velocity 
per minute. 

The question of determining the piston velocity is one of 
the vital points in the selection of an air compressor. Notwith- 
standing anything which may be said to the contrary, the most 
economical compressor is one which moves at a slow piston 
velocity and high piston velocities are only used to save initial 
expenditure. Therefore, when one contemplates the install- 
ment of a permanent air compressing plant or one which will 
likely be operated for one or more years, it is always better to 
select a low piston speed and pay the extra price for the larger 
machine which this entails, than to pay the extra fuel bill 
caused by a higher velocity. 

It is to be regretted that most purchasers do not understand 
the value of a low piston speed for an air compressor. A low 
initial price seems to be the principal virtue. There is not 
room enough in the ordinary cylinder diameter to give the 
proper ingress and egress of air under economical conditions. 
An indicator card from most compressors, running under a 
piston speed of 400 feet per minute, shows an enormous increase 
of pressure to force the air through the delivery valves, 
which, of course means a corresponding loss. The ideal indi- 
cator card is one which shows no suction pressure, and which 
shows that the delivery valves open at, or nearly at, the receiver 
pressure. Practically, this is not accomplished, and there are 
few, if any , compressor-builders proud of the indicator card taken 
from one of their compressing cylinders at such a piston speed. 
Yet their machines are forced to such speeds, oftener constantly 
than frequently. The writer has taken cards from various 
machines that showed 10 per cent of power used in forcing air 
through the delivery valves. It is not a simple matter to 
make a practical machine that shall work economically at 
high piston speed. It is at present far better practise to use a 
compressor at low piston speed and avoid those losses which 
cannot be recovered. The ideal system of compression is a 
continuous one, and while it seems almost impossible, the 
writer has already built one machine which gives fair promise, 
and future experiments will probably develop the question. In 
continuous compression there are no mechanical cylinder losses 
that amount to much. 

No compressor builder advocates high rotative or piston 
speed, and for the advancement of compressed air practise it is 
to be hoped that purchasers will consult operative expense 
rather than initial expenditure. 



8 4 



RIX AIR COMPRESSORS. 






















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RIX AIR COMPRESSORS. 



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86 RIX AIR COMPRESSORS. 

RIX DUPLEX STEAM ACTUATED 
COMPRESSOR. 

Cdass A, Fig. 32. 

Fig. 32 is a half-tone of the Rix Duplex Steam Actuated Com- 
pressor, of the flat bed type, having slipper cross head. 

Fig. 33 is a plan of this same machine, showing arrange- 
ments of foundation bolts and piping. 

Fig. 34 is an end elevation of the same compressor. 

Fig. 35 is a side elevation of the same compressor, and is at 
the same time a side elevation of the Single steam actuated 
compressor. 

Wherever possible, it is desirable to install a Duplex Air 
Compressor. The cranks being placed at right angles, the air 
is discharged more continuously throughout the whole revolu- 
tion, and the result is that the strains in the machine are more 
evenly divided and the machine as a whole gives better satis- 
faction . 

Another reason which should prompt a Duplex machine is, 
that should it be necessary to discontinue the use of one-half 
of the machine for repairs, the other half is always available 
and is a complete working compressor in itself. 

The following is a table of dimensions for these compressors: 

RIX DUPLEX STEAM ACTUATED COMPRESSOR. 

CLASS A. 

For Revolutions per minute, Cubic Feet Free Air, Rock 
Drill Capacity, see pages 84 and 85. 



No. 


Diameter 
Steam Cylinder. 


Diameter 
Air Cylinder. 


Stroke. 


H. P. 
Boiler. 


Price. 


I 


IO 


IO>'2 


14 


60 




2 


12 


l2 l / 2 


16 


80 




3 


14 


I4K 


18 


1IO 




4 


16 


16^ 


18 


140 




5 


18 


l8# 


24 


200 




6 


20 


2oy 2 


24 


2 O 


j 


7 


22 


22}i 


SO 


3IO 




8 


24 


24^ 


30 


400 





RIX AIR COMPRESSORS. 



87 




88 



RIX AIR COMPRESSORS. 




/ 1 



RIX AIR COMPRESSORS. 



8 9 




Fio. 34— Class A.— Rix Duplex Steam Actuated Compressor. 



9 o 



R1X AIR COMPRESSORS. 




RIX AIR COMPRESSORS. 



91 



RIX SINGLE STEAM ACTUATED 
COMPRESSOR. 

Class B, Fig. 36. 

The following half-tone, Fig. 36, shows the general style of 
construction of Class B, Rix Single Steam Actuated Compressor, 
and Fig. 35 shows the side elevation of same. 

This machine differs only from the Duplex Compressor in 
the fact that it is one-half of that machine and has an outboard 
bearing. 

The following is a table of the various and proper 

dimensions. 



RIX SINGLE STEAM ACTUATED COMPRESSOR. 

CI.ASS B. 

For Revolutions per minute, Cubic Feet Free Air, and Rock 
Drill Capacity, see pages 84 and 85. 



No. 


Diameter. 
Steam Cylinder 


Di^meter 
Air Cylinder. 


Stroke. 


H P. 
Boiler 


Price. 


9 
IO 
II 
12 
13 
14 
15 
16 


IO 
12 

14 
16 
18 
2 J 
22 
24 


ioy 2 

i6y 2 
isy 2 

2oy 2 
22^ 
24; 2 


14 
16 
18 
18 
24 
24 
30 
30 


30 

40 

55 

70 

IOO 

I30 

155 

200 





92 



RIX AIR COMPRESSORS. 



a m 





RIX AIR COMPRESSORS. 



93 



RIX SINGLE STEAM ACTUATED 
COMPRESSOR, SELF-CON- 
TAINED TYPE. 

Class C, Fig. 38. 

This machine is one which is offered to the mining public as 
the least expensive andmost generallyuseful machine of the kind 
ever constructed. It will be noted from the half tone that this 
consists of an independent standard engine on a bed-plate con- 
nected to an. air-compressing cylinder, the whole being tied 
together for proper operation. The engine is self contained, 
there being no outboard box, the fly wheel pulley being over- 
hung, so that this machine can be placed anywhere and is 
ready for operation at once. A belt can be placed upon the 
fly wheel pulley and be used to operate a pump or any other 
machine that may be desired while the compressor is not in 
use, in which case it will only be necessary to remove one inlet 
valve on each end of the air cylinder and the compressor end 
of the machine becomes inactive. 

This machine is especially built for prospecting, temporary 
work and for experiments, where a permanent plant is too 
expensive. It will' be noted, from the construction, that the 
engine can be entirely removed and used independently should 
occasion demand, and the whole arrangement is one which 
gives a prospector an opportunity to easily dispose of his 
machine should his mining venture prove a poor one. 

The following is the list of sizes of the Class C Compressor. 

RIX SINGLE STEAM ACTUATED COMPRESSOR, SELF- 
CONTAINED. 



For Revolutions per minute, Cubic Feet Free Air, and Rock 
Drill Capacity, see pages 84 and 85. 



17 
18 

19 



23 
24 
25 
26 

27 



Diameter Diameter 

Steam Cylinder Air Cylinder 



13 
14 
16 
18 




Stroke. 


H. P. 

Boiler 


IO 


15 


IO 


20 


12 


25 


12 


30 


14 


30 


14 


35 


16 


40 


16 


45 


18 


55 


20 


70 


22 


100 



94 



RIX AIR COMPRESSORS. 



¥■■ 




~»45M 




R1X AIR COMPRESSORS. 



95 

COM- 



RIX DUPLEX SHAFT- DRIVEN 
PRESSOR. 

Class D, Fig. 39. 

This half-tone represents one of the new style Shaft-Driven 
Rix Duplex Compressors, heavy duty style. This machine has 
Corliss frame, extra large wrist pins, and large cross head. 
The frame is swelled up on the front head so that the head 
may be removed without disconnecting the cylinder. The 
Compressor which was the subject for this half-tone was driven 
by a twelve-foot tangential water wheel, under a head of two 
hundred and seveuty-five feet. It may, however, be driven by 
belt. 

Fig. 40 is a side elevation of the same machine, showing 
belt pulley. 

Fig. 41 shows a sectional machine of the same class, but 
having a fiat bed, with water wheel attached upon the shaft. 

This Compressor, as all the sectional compressors herein- 
after mentioned, is made in sections not to exceed 325 lbs. in 
weight, so that they may be carried upon mules. 

The following table gives the sizes and principal dimen- 
sions for the Class D machines: 

RIX DUPLEX SHAFT-DRIVEN COMPRESSORS. 

CLASS D. 

For Revolutions per minute, Cubic Feet Free Air, and Rock 
Drill Capacity, see pages 84 and 85. 



No. 


Diameter 
Air Cylinder. 


Stroke. 


Price. 


28 


8 

10K 

13 


12 

14 
16 




29 

30 
31 
32 
33 
34 
35 
36 






16 y 2 i8 
18^ 24 

20^ 24 
22^ 30 

2A\4 "20 
4/2 













9 6 



RXI AIR COMPRESSORS. 




RIX AIR COMPRESSORS. 




9 8 



RIX AIR COMPRESSORS. 




RIX AIR COMPRESSORS. 



99 



RIX DUPLEX TANDEM SECTIONAL 
SHAFT-DRIVEN COMPRESSORS. 

Class E, Fig. 42. 

These Compressors are entirely similar to the Class D Ma- 
chines as noted in Fig. 4r, with the exception that the bed 
is extended and an additional air cylinder placed tandem to 
the others. This makes a very convenient form of machine, 
and one which gives a large air capacity with little additional 
weight. These air cylinders are so connected up that any one 
of the four cylinders, or any combination of the four cylinders, 
may be run together. The utility of this machine will be 
recognized at once. 

Fig. 43 is a side elevation of this Class E machine. 



RIX DUPLEX TANDEM SECTIONAL SHAFT-DRIVEN 
COMPRESSORS. 



For Revolutions per minute, Cubic Feet Free Air, and Rock 
Drill Capacity, see pages 84 and 85. 



No. 


Diameter 
Air Cylinder. 


No. of Air 
Cylinders. 


Stroke. 


Price. 


37 
33 
39 
40 


8 
I4# 


4 
4 
4 
4 


12 

14 
16 
18 













RIX AIR COMPRESSORS. 



y^iiJln* 




| 






J, be 



'" .-»J * 



' 



RIX AIR COMPRESSORS. 



hB>- 



H&- 



#o 



102 RIX AIR COMPRESSORS. 

RIX SINGLE SHAFT-DRIVEN 
COMPRESSOR. 

Ceass F, Fig. 44. 

This half-tone shows a flat bed type of compressor, but they 
are made also with Corliss frames, as shown in the Class D 
machines, Fig. 40, the smaller machines being made as per 
Fig. 44. This machine has an outboard bearing and may be 
driven either by belt, pulley, or by water wheel upon the shaft. 

Fig. 45 shows a side elevation of this Class F compressor. 

The following is a table of the sizes and general dimensions 
of this style of air compressor: 



RIX SINGLE SHAFT-DRIVEN COMPRESSOR. 

CEASS F. 

For Revolutions per minute, Cubic Feet Free Air, and Rock 
Drill capacity, see pages 84 and 85. 



4i 
42 
43 

44 
45 
46 
47 
48 

49 



Diameter 
Air Cylinder. 



E3 
14>2 

i6y 2 



H 
16 
18 
iS 
24 
24 



KIX AIR COMPRESSORS. 



I0 3 




io4 



RIX AIR COMPRESSOR 




RIX AIR COMPRESSORS. 



I05 



RIX COMBINED DUPLEX STEAM 
ACTUATED AND SHAFT- 
DRIVEN COMPRESSOR. 

(Xass G, Fig. 46-46^. 

This is a form of compressor which is especially adapted to 
the wants of the Pacific Coast, where there is abundance of 
water supply during one portion of the season and an insuffi- 
cient supply during the remainder. It becomes, therefore, 
necessary to run the compressor with water power during a 
portion of the year, and steam power during the balance. 

It will be noted from the half tone that the air cylinders 
are placed next to the water wheel, which water wheel has 
been built upon the fly wheel of the machine, the steam 
cylinders being tandem to the air cylinders, with a sleeve 
coupling between. When it is desired to run by water power 
it is only necessary to remove the sleeve coupling, and the 
machine becomes a water power compressor. The couplings 
may be replaced in an hour, at any time, and the machine 
again converted into a duplex steam machine, using the com- 
bined fly wheel and water wheel for a fly wheel. 

These compressors are made in the following sizes: 

RIX COMBINED DUPLEX STEAM ACTUATED AND 
SHAFT-DRIVEN COMPRESSOR. 



For Revolutions per minute, Cubic F'eet Free Air, and Rock 
Drill Capacity, see pages 84 and 85. 



No. 


Diameter 
Steam Cylinder 


Diameter 
Air Cylinder 


Stroke 


H. P. 

Boiler 


Price 


50 

51 

52 

53 

54 

55 

56- 

57 


IO 
12 
14 
16 
18 
20 
22 
24 


I2# 
16% 

isy 2 

2oy 2 
22 i y 2 
24^ 


14 
16 
18 
18 
24 
24 
30 
30 


60 
80 
no 
140 
200 
260 

310 

400 





io6 



RIX AIR COMPRESSORS. 






i\ 




RTX AIR COMPRESSORS. 







I08 RIX AIR COMPRESSORS. 



RIX STEAM ACTUATED VERTICAL 
COMPRESSORS. 

Ceass H, Fig. 47. 

This style of compressor is one which has given universal 
satisfaction in this State, a machine of similar type having run 
continuously from 1880 to the present date with no expense 
whatever beyond valve springs. It is single acting; the air 
cranks being placed at 180 degrees from each other, which 
balances the machine completely, and the cylinders being ver- 
tical there is no internal wear of any consequence. The steam 
engine is placed horizontally on the floor, for the double pur- 
pose of keeping the warmth of the steam cylinder away from 
the inlet air, and also for the purpose of making the steam 
crank at right angles to the air cranks. 

This compressor is made in only one size: 12-inch steam 
cylinders, 12^-inch air cylinders by 16-inch stroke, and 
catalogued No. 58. Capacity in free air per minute, see page 
84, both cylinders being the equivalent of one double-acting 
12^-inch cylinder, as per table. 

Figs. 48, 49, and 50 show different views of this same 
machine. 



RIX AIR COMPRESSORS. 



I09 




. 47— Class H.— Rix Steam Actuated Vertical Compressor. Manufactured 
by Fulton Engineering and Shipbuilding Works, San Francisco. 



RIX AIR COMPRESSORS. 




Fig. 48— Class H.— Rix Steam Actuated Vertical Compressor. Manufactured by 
Fulton Engineering and Shipbuilding Works, San Francisco. 



RIX AIR COMPRESSORS. 







Fi3. 49— Class H.—Rix Steam Actuated Vertical Compressor. Manufactured 
by Fulton Engineering and Shipbuilding Works, San Francisco. 



RIX AIR COMPRESSORS. 




Fig. 50— Class H.— Rix Steam Actuated Vertical Compressor. Manu- 
factured by Fulton Engineering and Shipbuilding Works, 
San Francisco. 



RIX AIR COMPRESSORS. 



113 



RIX SINGLE CORLISS ACTUATED 
COMPRESSORS. 

Class I, Fig 51. 

These Compressors consist of a Standard Corliss engine, to 
which there is placed tandem the air cylinder. 

Fig. 52 shows a plan of the single machine. They are an 
economical and high-class machine in every respect. 

The following table shows the sizes and dimensions of the 
Class I,;Rix Single Corliss Actuated Compressors: 

RIX SINGLE CORLISS ACTUATED COMPRESSORS. 

CLASS I. 

For Revolutions per minute, Capacity Free Air, Rock Drill 
Capacity, see pages 84 and 85. 



59 
60 
61 
62 
63 
64 

65 
66 

67 
68 
69 
70 
7i 
72 

73 
74 



St'm Cylinder. 



16 
16 
16 
16 
16 
16 
18 
18 
18 
18 
]8 
18 



Diameter 
Air Cylinder. 



12^ 

i6# 

16^ 
i8# 

18K 
16^ 
i8# 
i8# 

20>£ 

iSj4 
2o>£ 
18K 
20K 



30 
30 
30 
30 
30 
30 
36 
36 
42 
42 
36 
36 
42 
42 
48 



RIX AIR COMPRESSORS. 




RIX AIR COMPRESSORS. 




Il6 RIX AIR COMPRESSORS. 

RIX COMPOUND CORLISS ACTUATED 
COMPRESSORS. 

Class J comprises the Rix Compound Corliss Acttiated Com- 
pressors^ which are entirely similar to those of Class I excepting 
that the steam cylinders are compound, the air cylinders being 
alike. 

The following is a table showing the sizes and principal 
dimensions of the Class J Compressors: 

RIX COMPOUND CORLISS ACTUATED COMPRESSORS. 

CEASS J. 

For Revolutions per minute, Cubic Feet Free Air, Rock 
Drill Capacity, see pages 84 and 85. 



No. 


Diameter High 
Pressure. 


Diameter Eow 
Pressure. 


Diameter Air 
Cylinder. 


Stroke. 


Price. 


75 


12 


22 


12^ 


30 




76 


12 


22 


14^ 


30 




77 


f4 


26 


14^ 


30 




78 


14 


26 


16^ 


30 




79 


16 


30 


l6>^ 


30 




80 


16 


30 


l8>^ 


30 




81 


16 


SO 


16^ 


36 




82 


16 


30 


i8/ 2 


36 




83 


16 


30 


16^ 


42 




84 


16 


30 


isy 2 


42 




85 


18 


34 


isy 2 


36 




86 


18 


34 


20 l / 2 


36 




87 


18 


34 


isy 2 


42 




88 


18 


34 


20 l A 


42 




89 


18 


34 


isy 2 


48 




90 


18 


34 


2oy 2 


48 





Both the Compressors Class I or Class J are furnished either 
condensing or non-condensing. 



RIX AIR COMPRESSORS. 



RIX LIGHT DUTY COMPRESSOR OR 
VACUUM PUMR 

Ci,ass K, Fig 53. 

This Compressor is adapted for very light work and is a 
self-contained machine working from a Scotch yoke. It is 
intended for pressures up to 25 lbs. only, and can be either 
used as a compressor or a vacuum pump, the valves being 
arranged for that purpose. It is single acting and the dis- 
charge is absolutely complete, there being no clearance what- 
ever. It is capable of creating a 2g-inch vacuum. 

Made in four sizes having 4 7/ , 5 /7 , 6 // , and 7 7/ diameter of 
cylinders, and catalogued No. 91, 92, 93, and 94 respectively. 

This machine is a very inexpensive and satisfactory com- 
pressor to have in laboratories, shops, and canneries, or for 
blowing crude oil into furnaces. A four-inch belt is ample to 
run any of them. The peculiar feature which is advantageous 
as a vacuum pump is the discharge valve which covers the 
whole end of the cylinder. The piston touches it, moves it 
slightly from its seat, thus dispelling all the air, the valve 
reseating as the piston begins the return stroke. 



RIX AIR COMPRESSORS. 




Fig. 53— Class K.— Rix I^ight Duty Compressor or Vacuum Pump. 






RIX AIR COMPRESSORS. 119 



RIX STEAM ACTUATED DUPLEX 
COMPRESSORS. 

Class Iv. 

These compressors are designed for compressing air to not 
exceeding twenty-five pounds per square inch, with a steam 
pressure at from sixty to ninety pounds. They are made with 
Scotch Yoke, as may be seen from the cut in Fig. 54, and are 
self contained in every respect. They are especially adapted 
for this Coast, for furnishing air for burning crude petroleum 
or distillate. 

These machines are far heavier and stronger than any 
machine which is built in the East for the same purpose; the 
same comparative cylinder sizes being made about twenty-five 
per cent heavier, so that for use on shipboard they may be 
absolutely relied upon not to break or give out when at service. 

These machines are complete with all lubricators, valves, 
and also automatic governor, which will regulate the machine 
to within two or three pounds of the receiver pressure. 

Kach one of these compressors is set up in the shop and 
thoroughly tested before shipment, so that the machine will be 
ready to go to work as soon as set upon its foundations. 

The following are the sizes of the Rix Steam Actuated Duplex 
Compressors, Class L ; 



RIX AIR COMPRESSORS. 




RIX AIR COMPRESSORS. 



RIX STEAM ACTUATED SINGLE AIR 
COMPRESSORS. 

Cl,ASS M. 

These machines are precisely like those of Class L,, except- 
ing that they are Single instead of Duplex, and are fitted up in 
precisely the same manner. 

They are complete with governor, lubricators, oilers, and 
wipers. 

Each machine is tested before leaving the shop, so that it is 
ready for work immediately it is erected upon its foundations. 

The following are the sizes of the Rix Steam Actuated Single 
Air Compressors, Class M : 



RIX AIR COMPRESSORS. 



-ISAIOJ 3SJOH 



•3irxnxj\[ asd 
axy aa-itf }3<3^[ oxqn^ 



10 r^ 



O ro O 






•saqoui 

lit 3§-lBipSI(I J.IV 



W rO 



•saipui m l-snxi axy 



CN O Ol <T> 



•saxpixi 
in }sixbi[Xk£ xxxBais 



•saxpui 
UT Arddng uxB3is 



•saqoui 
ux s^oa^e; jo xj.}£ii3l 


vO 


r-» 


i>» 


o> 


C^ 


C^ 


•saipxxi ux .xapixx 

•\&d JXV J313XXXBXQ 


^O 


t^ 


CO 


On 


O 


^h 


•S3X|0UI xxi japux 
-1^0 uiBaas ab^aaxBia 


^t- 


to 


lO 


v£> 


!>. 


o> 



RIX AIR COMPRESSORS. 



123 



J3MOJ 3SJOH 



04 ro rO IO 






jad snopnxoAa-a 



•saipui 
in 3g.reipsia -»V 



« ro 



•saqoui ni ^\uj axv 



OJ CN CS rO 



■S3XIDUI 
III ^sriBuxjj xuBa;s 



•S3t[0UI 

ux Xjddns raB3;s 



>S 



•S3H0UI 


MD 


r^ 


r^ 


o\ 


c^ 


On 


•saxpni in jap 
-uyi^o jiy Jajauma 


VD 


t^ 


CO 


a\ 





"* 


•saipni in japin 


"* 


to 


10 


vo 


t^ 


On 



124 



■RIX AIR COMPRESSORS. 




Class N, Fig. 54— Duplex Direct Acting Steam Actuated Compressors. 



DUPLEX DIRECT ACTING STEAM 
ACTUATED COMPRESSORS. 

Ceass N. 

It will be noted from the cut, Figure 54, that these com- 
pressors are made after the style of the DIRECT ACTING 
STEAM PUMP, and they are designed to meet certain require- 
ments where light pressures and inexpensive or temporary 
machinery are desired. They are the least expensive of all com- 
pressors which are built, and while they do not have a very 
high volumetric efficiency, they are easily installed and for cer- 
tain classes of work are amply economical. 

The AIR CYLINDERS are composition lined and the PIS- 
TON rods are of brass. Every machine is fitted complete with 
its PROPER LUBRICATOR and wrenches. The VALVE 
MECHANISM is so arranged that the air pistons work against 
a constant pressure at all times, thus obtaining quite a high 
efficiency for this character of compressor, and insuring a uni- 
form stroke. 

There are no DEAD CENTERS on the machine, and the 
pump is consequently always ready to start. The dispensing 
of the crank and flywheel renders it possible to place this com- 
pressor in an extremely small space. 



RIX AIR COMPRESSORS. 1 25 

The VALVES in the steam end are slide valves, and in the 
air and poppet valves of the ordinary type positively con- 
trolled by the valve mechanism. The entire apparatus is com- 
pact, durable, and self-contained. There are no intricate 
working parts whatever, and it requires very little attention 
to operate it. 

As a general rule it is desirable to operate this machine in 
connection with a PRESSURE REGULATOR, which we fur- 
nish with the machine if desired. The PRESSURE REGU- 
LATOR automatically controls the speed, slowing down and 
finally stopping the pump when the desired air pressure is ob- 
tained, and gradually starting up again when the air is ex- 
hausted from the reservoir. This regulator practically makes 
the machine automatic in its operation. 

This Compressor is used in BREWERIES for BEER 
RACKING, and is especially desirable for that purpose. It is 
also used in running PNEUMATIC TOOLS for cutting mar- 
ble or granite, or other building stone, and also for CHIPPING 
and CALKING BOILERS; for the running of SAND BLASTS; 
for the handling of ACIDS in refineries; for running small 
PNEUMATIC CRANES; for use in RUBBER FACTORIES, 
or for pumping pressures upon AUTOMATIC FIRE EXTIN- 
GUISHERS; for CLEANING CARS where a jet of air is used 
to dust off cushions it is especially valuable as an inexpensive 
and cheap machine; for the running of CLIPPING MA- 
CHINES, or for running COAL CONVEYORS, or SMALL 
ROCK DRILLS, where pressures not exceeding fifty or sixty 
pounds are required; for PNEUMATIC EJECTORS, or for 
producing vacuums for FILTERING purposes; and the enum- 
erable requirements where low pressure compressed air is 
desired. 

For RUNNING ROCK DRILLS we do not advocate it for 
a permanent plant, but for a prospecting plant for small drills, 
these compressors can be readily installed and will prove first- 
class in their operation. 

These Compressors are particularly adapted for furnishing 
the compressed air to BURN PETROLEUM COMPOUNDS 
UNDER BOILERS FOR GENERATING STEAM. 



126 



RIX AIR COMPRESSORS. 



DUPLEX DIRECT ACTING COM- 
PRESSORS. 

Class N. 

Capacities calculated on piston speed of 60 feet and volu- 
metric efficiency of 70 per cent. 



No. 


S s si 

a-M a 


g«J a 
Q U 


© 
35 


Cubic Feet 

of 
Free Air. 


<U g D 
(D.gE 

w 


6 

CO u 

< 


94: g 


Price. 


107 


4X 


3 


4 


2.07 


% 


% 


60 




108 


4^ 


4 


4 


3-68 


X 


X 


50 




109 


4K 


4X 


4 


4-65 


X 


X 


40 1 


no 


5X 


3 


5 


2.07 


X 


I 


60 




III 


5>4 


3X 


5 


2.8l 


X 


I 


50 




112 


5X 


4 


5 


3.68 


X 


I 


50 


113 


5X 


4X 


5 


4-65 


X 


I 


45 


114 


5X 


4X 


5 


5.o6 


X 


I 


40 


115 


5X 


6 


5 


8.28 


x 


I 


20 


Il6 


6 


3 


6 


2.07 




IX 


70 


117 


6 


3^2 


6 


2.8l 




iX 


60 


Il8 


6 


4 


6 


3-68 




*x 


55 


119 


6 


4X 


6 


4.65 




iX 


50 


120 


6 


4X 


6 


5.06 




iX 


45 




121 


6 


6 


6 


8.28 




iX 


40 




122 


6 


6^ 


6 


9.70 




iX 


30 


123 


6 


7 


6 


II.27 




iX 


25 


124 


6 


7X 


6 


13. 




iX 


20 




125 


6 


8 


6 


14.72 




iX 


15 





RIX AIR COMPRESSORS. 127 



PNEUMATIC GOVERNORS. 

Fig. 54/^ shows the Pneumatic Governor which the Fulton 
Engineering Company attach to all the Corliss Compressors. 
This Governor consists in a special attachment arranged in 
connection with the Standard Corliss Governor, which is 
actuated by the air pressure. When the pressure rises in the 
air receiver the Governor balls are automatically lifted and 
the hooks are thus tripped independently of the number of 
revolutions which the engine is making. When the pressure 
falls in the tank the device drops out of the way and the 
engine is controlled by the Corliss Governor pure and simple. 

For all ordinary compressors, when desired, a Governor is 
furnished which controls the admission of steam readily as the 
load varies. It is simple and effective in its operation. 



128 



RIX AIR COMPRESSORS. 




gfc 



u.9 



THE RIX COMPOUND COMPRESSOR. 



In speaking of the various means in practise for cooling 
the air during its compression, reference has been made here- 
tofore in this treatise to compounding the compressing cylin- 
ders. The advantages of this process are so important that it 
has come into general use and Compound Compressors nowa- 
days are beginning to be the rule rather than the exception. 
It is therefore interesting to give some explanation of this 
method of compression. 

The principle of Compound Compression can be described 
as follows: Suppose that a certain volume of air at atmospheric 
pressure and temperature is to be raised to a certain pressure 
and delivered into a receiver; in ordinary, or single stage 
compression, this air is introduced into a cylinder wherein a 
piston effects the compression and delivery of that air at each 
stroke. This compression, as we know, and especially in fast 
moving machines, is accompanied by a considerable develop- 
ment of heat, which causes a loss of efficiency. 

In the compound machine, air is adm tted into a cylinder, as 
before, but it is compressed and delivered into a receiver at a 
pressure smaller than the desired final pressure. In this first 
period or stage of compression there is a certain amount of 
heat developed, less, however, than in the single stage ma- 
chine. The compressed air, after it is delivered into this first 
receiver at the intermediate pressure, is cooled by coming in 
contact with a number of copper tubes through which cold 
water is rapidly circulated. This receiver is quite similar to 
the surface condenser used in marine engines and is termed 
the Intercooler, and the compressed air leaves it after having 
been deprived of its heat, and reduced to practically the tem- 
perature of the water. It is then admitted into another smaller 
cylinder wherein its pressure is raised by another piston — the 
air being again passed through another intercooler — then ad- 
mitted into a third cylinder, and so on until the final desired 
pressure is reached. 

The compression of air, instead of being affected all at once, 
is therefore performed in several stages, each separated from 
the following one by a cooling to the atmospheric temperature. 
It may be readily conceived that the partial amounts of heat 
developed in this series of cylinders are more effectively dealt 
with than when the whole amount of heat is liberated in a 
single cylinder. On this ground the Compound Compressor 
will therefore possess a higher efficiency than the single stage 
machine. 

Another advantage is that the variation of load on the 
piston during the stroke is less in the compound, and conse- 
quently the strains on the crankpins are reduced, and a lighter 



130 



THE RIX COMFOUND COMPRESSOR. 




THE RIX COMPOUND COMPRESSOR. I3I 

flywheel will regulate the motion of the machine than is the 
case in a single-stage compressor. For instance, if we use a 
12-inch cylinder to compress air to 100 lbs. gauge, in the single- 
stage compressor, the load on the piston during one stroke 
will vary from o to 11,300 lbs., whereas in the compound ma- 
chine this load can be made to vary from o to 5960 in all. 

The principle of the Compound Compressor applies to any 
number of successive stages, and, theoretically, the more 
stages there are used the nearer will the compression approach 
the isothermal. But, at a practical standpoint, the increased 
number of cylinders is, of course, objectionable, inasmuch as 
it makes a heavier and more intricate machine, which will cost 
more and necessitate more expenditure for maintenance. The 
frictional resistances also become greater with the number of 
cylinders, and it is, therefore, readily seen that there are some 
practical limitations in the use of this system. 

It may be stated that for pressures not exceeding 200 and 
even 300 lbs. per square inch, there should not be more than 
two stages in the compression. Four stages is the limit which 
has not been thus far exceeded, even with air pressure reach- 
ing to 2000 lbs. per square inch, and even for these high pres- 
sures three-stage compressors are deemed amply sufficient. 

On the other hand, the compound system would be an 
unnecessary improvement with low pressures. For 50 or 60 
lbs. receiver pressure it is quite likely that the percentage of 
extra resistances would balance if not overcome the percentage 
of gain in cooling. 

In general, the advantages of a compound system consist in 
that less heat is developed at each stroke of the piston, while 
the air under compression is exposed to a larger cooling sur- 
face than in a single-stage machine. 

The diagram, Fig. 56, represents the theoretical adiabatic 
cards of a 12x16 single stage compressor and of a tandem com- 
pound 12 and 73^x16, both compressing to 70 lbs. gauge. It 
also shows the expansion curve in a 12x16 steam cylinder de- 
veloping with steam at 80 lbs. gauge the same work as the 
single stage compressor. 

These cards do not show the variations of pressure of steam 
and air, but the variations of effective load on the piston rod 
of the three cylinders, and they will serve for a comparison of 
two direct-acting steam compressors — one in the single stage 
and one in the compound system. 

We know already that the aggregate piston load in the com- 
pound is less than in the single machine and as the initial 
loads are o in both cases, the range of variation is less in the 
compound. This allows a reduction in the size of the piston 
rods. It will be noticed that the compound curve has a sharper 
rise, since the maximum load H. G. is reached at the point / 
of the stroke, while in the single cylinder this same load is 
only reached at the pointy. The result of it is that during 
this portion of the stroke, which precedes the point of equal 
loads in the two compressors, i. e., the point of intersection of 



132 



THE RIX COMPOUND COMPRESSOR. 




THE RIX COMPOUND COMPRESSOR. 



133 



the steam and air curves, the difference of the load between the 
steam and air pistons is smaller in the compound, where it is 
6" V for instance, than in the single cylinder compressor, 
where at the same point T, of the stroke, the difference is 
5 V. 

The same may be said for the second portion of the stroke, 
except in the region// 7 , but here the discrepancy is unim- 
portant, the piston loads being but little at variance in the two 
compressors, and this region corresponding to the maximum 
velocities of the pistons. 

As the mass of moving pieces, whose momentum is resorted 
to for securing a regular motion, is a function of the actual dif- 
ference between the steam air piston loads, lighter regulating 
pieces, like flywheels, will be required in the compound than 
in the single compressor. 

The same size of steam cylinder will be found adopted in 
practise with both kind of compressors, the point of cut off 
being, moreover, variable. 

A longer expansion of steam, combined with a less weight 
of machine, combine to win for a compound compressor the 
deserved claim of being a better balanced and more economi- 
cal machine than the single stage. 

It will be seen that a proper design of such machines must 
tend to an equal division of the total work among the several 
cylinders; that the loads are equal on each one of the pistons 
at any point of the stroke, and that the temperature of the 
entrance and exit of the air are the same in all the cylinders. 

The following table shows the percentage of gain obtained by 
compounding as against the single-stage system, with various 
modes of compression: 

PERCENTAGE OF GAIN OF 2-STAGE VS. I-STAGE SYSTEMS OF 
COMPRESSION. 



Ratio of Receiver pressure to atmos- 
pheric pressure. 



Gain per cent in: 
Adiabatic Compression (no cooling). 
Jacketed Cylinders 



Jacketed Cylinders cooled by spray in- 
jection in the most efficient way 
possible 



n-5 

8-95 

6.4 



12.5 



13-8 



14.8 
11. 8 



7 5 8.2! 8.7 



15.9 
12.5 



9.2 



These figures show that for the usual air pressures the 
amount of work saved by compounding varies from 9 to 12 
per cent. This is by no means a quantity to be neglected. 



134 The rix compound compressor. 

We also note that the advantage of compounding increases 
with the pressure and is more marked with a poor than with an 
improved system of cooling. 



The Fulton Engineering and Shipbuilding Works do not 
issue a list of the various sizes of their Compound Compressors, 
for the reason that the relation between the two cylinders can 
never be fixed, the sizes of the initial cylinders depending of 
course upon the quantity of air required, and the size of the 
compound cylinders depending entirely upon the pressure 
desired. Special estimates and specifications are furnished 
with each compound machine. The following illustrations 
show some of the compound machines built by the Fulton 
Engineering and Shipbuilding Works, and give an idea of 
their general style. 

The Compound Compressor, Fig. 60, shown in the preced- 
ing cut, illustrates the general style of the Compound Com- 
pressors built by the Fulton Engineering and Shipbuilding 
Works. This Compressor was built for the North Star Mining 
Company, of Grass Valley, Cal., and consists of Duplex Tan- 
dem Compound machines. The initial cylinders are 18 inches 
in diameter, and the high pressure cylinders are 10 inches in 
diameter by 24-inch stroke. The piston speed of the machine 
is 440 feet, which, while not quite as economical as one much 
lower, was dictated by the conditions under which the water 
wheel operated. 

The air enters the initial cylinder at the temperature of the 
power room, which is approximately 62 degrees, and is therein 
compressed to 25 lbs. to the square inch gauge pressure. It 
leaves the cylinder at a temperature of 200 degrees Fahr. and 
passes through an intercooler of about 1000 running feet of 1- 
inch copper tubes placed directly beneath the water wheel, and 
which receives from the wheel a continual shower of water at a 
temperature of about 58 degrees. This cools the air to such an 
extent that it is delivered to the high pressure cylinders at a 
temperature of about 60 degrees. In these cylinders the air is 
compressed to 90 lbs. and is delivered from the cylinders at a 
temperature of 204 degrees into 6-inch mains, which lead to the 
mine. Indicator cards taken from the cylinders show that the 
cylinders are doing equal work, and at no revolutions they 
work smoothly and perfectly. 

Notwithstanding the fact that some builders claim that 
clearance has no detrimental effect upon the economy of their 
air compressors, in the Rix compressors the clearance is prac- 
tically eliminated, being not to exceed one-thirty-second of an 
inch at each end of the stroke. The cards taken from these 
cylinders are practically square-cornered. 

The water-jacket system is quite unique, it being a duplex 
system — that is, there is an independent circulation for each 
end of the cylinder, the water passing longitudinally back and 
forth on the side of the cylinder and from the center in two 



I' 



THE RIX COMPOUND COMPRESSOR. 



135 



-|s 



^ssj 



-i=- 



# 



136 



'The: rix compound compressor. 




THE RIX COMPOUND COMPRESSOR. 



137 




138 



the; rix compound compressor. 




THE RIX 'COMPOUND COMPRESSOR. 139 

independent streams, cooling the heads at the same time. The 
efficacy of this water jacket will be noted in the temperatures 
above given. 

In testing for volumetric efficiency, the receivers were care- 
fully measured a number of times and found to contain 291 
cubic feet. These were filled repeatedly, and the number of 
revolutions of the machine accurately counted each time. All 
of these experiments were conducted after the machine had 
been in operation for a sufficient length of time to reach its 
maximum temperature. 

The barometer at the power house is 27.35 inches, corre- 
sponding to an elevation of about 2400 feet. This gives an 
atmospheric pressure of 13.32 lbs. per square inch. At 90 lbs. 
gauge pressure the ratio of compression would be 7.7, and the 
receiver containing 291 cubic feet represents 2240 cubic feet 
capacity of free air. The average of a great many experiments 
showed that the compressor took 102^ revolutions to fill the 
receiver from 25 lbs, which is the pressure of the initial cylin- 
der, to 90 lbs. At this pressure of 25 lbs. gauge there is 830 
cubic feet of free air in the receiver. The difference between 
these two capacities, or 1410 cubic feet, would represent the 
imount of air which was forced into the receiver at the revolu- 
tions stated. Inasmuch as the temperature of the receiver is 
somewhat higher than the temperature of the inlet air, there 
should be a deduction made from this sum corresponding to 
that temperature of about two per cent, making the corrected 
amount delivered to the receiver 1382 cubic feet. 

The theoretical capacity of the compressor, deducting the 
piston rods, and at 102^ revolutions, is 1429 cubic feet of free 
air per minute. The ratio between 1382 cubic feet, actually 
delivered, and 1429 cubic feet, theoretical capacity, is 96.6 per 
cent, which represents the actual volumetric efficiency of the 
machine at the present writing. This of course will vary pro- 
portionately with the ratios of the absolute temperatures of the 
inlet air, depending upon the season of the year. 

One peculiarity about the Rix Compressor, as may be noted 
from the cut, is the fact that the compressor is so arranged that 
any cylinder may be disconnected or any end of any cylinder 
may be disconnected without interfering with the operation of 
the machine. This feature is very valuable in case of repairs 
or accident to the machine. 

To drive this compressor there has been placed upon the 
main shaft a Pelton water wheel, eighteen feet in diameter, 
which is believed to be the largest tangential water wheel ever 
made. 



THE PNEUMATIC TORPEDO PLANT 
AT THE PRESIDIO. 

(Originally published in "Journal of Electricity," S. F.) 

The recent tests made by the military authorities on the 
dynamite guns at Fort Point may lend some interest to a few 
particulars regarding the Air Compressing Plant which forms 
the vital element of this installation. 

The contract for the construction of the mechanical part of 
it, with the exception of the guns and their immediate fixtures, 
was awarded by the Pneumatic Torpedo and Construction Com- 
pany of New York to the Fulton Engineering and Shipbuild- 
ing Works of this city, upon the plans and special designs of 
Mr. E. A. Rix, who supervised the construction of the plant. 

The compression of" air is made in three stages, from the 
atmosphere to the working pressure of 2000 lbs. effective per 
square inch. It is performed in two sets of horizontal engines, 
to both of which the subsequent description applies, they being 
in all respects entirely alike. The steam is supplied by four 
boilers of the Horizontal Tubular type, of 750 H. P. capacity, 
arranged to work either with natural or with forced draught. 

Two steam cylinders connected to the same shaft by cranks 
at an angle of 145 degrees from each other, actuate in tandem, 
that is, through their piston tail rods, each two air cylinders, 
there being on one side one low pressure and the intermediate 
or second stage cylinder, and on the other side one low pres- 
sure and the high pressure or finishing cylinder. 

This duplex set therefore comprises two steam cylinders, 
two intake cylinders, wherein the atmospheric air is compressed 
to about 75 lbs. effective, one intermediate cylinder, carrying 
the air pressure from 75 to about 400 lbs. effective, and one high 
pressure cylinder, which takes the air at 400 lbs. and com- 
presses it to 2000 lbs. effective. 

The intake or low pressure cylinders are double acting, that 
is, they have inlet and discharge valves at each end, while the 
intermediate and high pressure cylinders are single acting, that 
is, provided with valves at one end only, their pistons being 
plunger rams with spherical heads, connected to the tail rods 
of the intake cylinders. 

The special purpose which these compressors have to serve 
made their design and construction subservient to conditions 
at entire variance with the lines upon which an air compressing 
plant is usually established. The main object of the designer, 
when a large power is to be used, as in the case of the Fort 
Point installation, is commonly to secure the greatest possible 
economy in the production of the compressed air. In the pres- 
ent instance, compound condensing engines of the most 
approved type, and air cylinders working at a moderate linear 



THE PNEUMATIC TORPEDO PI<ANT. 



141 




THE PNEUMATIC TORPEDO PEANT. 




THE PNEUMATIC TORPEDO PEANT. 



143 




144 THE) PNEUMATIC TORPEDO PLANT. 

piston speed, would present themselves to the mind as advis- 
able. Such engines would be established in view of a regular 
working speed, or approximately so, and everything would be 
provided to give the economical appliances a chance to work to 
their full advantage. 

At Fort Point the primary requirement was to have a plant 
as little liable as possible to getting out of order. Solidity 5 
simplicity, and endurance were therefore the main points to be 
considered, economy being a desirable but decidedly an acces- 
sory feature. 

Upon these general lines, supplemented by conditions of 
capacity within a given time, of efficiency in the means of cool- 
ing the air and of practical effectiveness of several important 
parts, the present plant was designed, built, and erected. 

The steam engines are non-condensing and each cylinder 
acts independently; that is, no compounding has been adopted. 
The valves are provided with Meyer's cut-off, regulated by 
hand, the Governors merely acting on the throttle in case 
of racing. The cranks are set at the angle heretofore 
indicated, in order that the machine may be balanced as nearly 
as possible and yet the engines be able to start in any position. 

In the air cylinders the greatest care has been used to 
secure a cooling efficiencv as high as possible. The heads and 
the barrels of the cylinders are water-jacketed, the water dis- 
charge pipes from the jackets being in full view and easily 
accessible, and the supply of cooling water being regulated 
according to its temperature at the discharge. 

A very elaborate and effective system of intercoolers has 
been established between the intake and intermediate cylinders 
and also between the intermediate and high pressure cylinders. 
These intercoolers consist of nests of copper pipes extending 
under the floor in cemented trenches, where a stream of cold 
water is constantly running. The proportions of these inter- 
coolers have purposely been made very ample, and their effect- 
iveness is fully demonstrated by the low temperature of the 
air before it enters the intermediate and the high pressure 
cylinder, which are given hereafter. 

A similar cooler is provided for the air at working pressure 
after it leaves the high pressure cylinder and before reaching 
the 24 forged steel storage tubes, which through a complete 
system of pipes and manifolds, and also a compact arrangement 
of valves, can be set in communication with each particular 
gun, or if so desired, with a supplementary storage supply 
located in the foundation of the guns. 

That the demand upon the compressors may vary during 
action, within widely distinct limits, was exemplified by the 
fact that while 360 feet per minute is generally considered as a 
limit of piston velocity in water jacketed cylinders, this velocity 



THE PNEUMATIC TORPEDO PLANT. 



145 




146 



THE PNEUMATIC TORPEDO PLANT. 




THE PNEUMATIC TORPEDO PLANT. 1 47 

has been, during part of the trials, carried to 568 feet, or an 
excess of 58 per cent. At this high rate of speed no undue 
heating could be observed in the moving parts and the absence 
of jarring and of trepidations was the best evidence of the 
remarkable strength and steadiness of the plant. 

Of course, when working at high speed, no claim is nor 
could be entertained to maintaining a satisfactory cooling 
efficiency in each individual cylinder. As before stated, the 
intercoolers are of sufficient size to deal with the heat liberated 
during the compression even at high speed. But when the 
period of compression, and, of course, the period of effective 
possible cooling, lasts two-fifteenths of a second, the heat units 
passing through the cylinder walls during that time cannot be 
expected to be many. It might be argued that the Riedler 
compressors in Paris work at a nominal piston velocity of 550 
feet and occasionally 733 feet per minute, but aside from the 
fact that the use of a spray for cooling and of mechanically 
moved valves are both combined to reduce the rise of temper- 
ature, the pressures in the two-stage Riedler compressor are 
considerably lower, the air being sent into the mains at only 
118 lbs. gauge per square inch, an insignificant pressure as 
compared to 2000 lbs. 

Another point of interest in the Fort Point plant is the 
absence of leakage at the stuffing boxes of the intermediate and 
high pressure rams. This point has been the cause of much 
annoyance in similar plants built elsewhere, and the present 
arrangement is the outcome of long and costly experiments. 

The friction, in a running joint capable of holding 2000 lbs. 
of air pressure against the atmospheric, is necessarily enor- 
mous, and after the nature, the shape, and the size of the 
packing had been determined upon, it became necessary to 
keep the packing sufficiently cool to prevent its rapid wear. 
This is effected by a special circulation of cold water inside the 
rams, the arrangement being quite apparent on the general 
plan, and that it is successfully effected can be easily ascer- 
tained. This water circulation also partly contributes to cool- 
ing the air under compression. 

At the normal rate of speed of about 400 feet per minute of 
piston velocity, the compressors supply to the storage tubes 
460 cubic feet of air per hour at 2000 lbs. gauge. The annexed 
abstract from trials made in view of timing the production of 
the compressors gives interesting evidence of the effectiveness 
of the intercoolers and of the regularity of the temperature of 
air at its entrance to each cylinder. 

For a range of final pressures comprised between 800 and 
2000 lbs. effective, the variation of temperature was only 8 
degrees Fahr. for the intermediate and 3 degrees Fahr. 
for the high pressure cylinder, the temperature of the engine- 
room being 71 degrees Fahr. 



148 



THE PNEUMATIC TORPEDO PI,ANT. 




THE) PNEUMATIC TORPEDO PEANT. 



149 




150 



the; pneumatic torpedo pivANT. 



Gauge pressure 


Fahr. 


temperature at entrance to 


lbs. per sq. in. 






E. P. Cylinders. 


I. P. Cylinders. 


H. P. Cylinders. 


800 


71 


67 


66 


900 


71 


68 


6 7 


IOOO 


71 


69 


67 


I IOO 


71 


69 67 


I200 


71 


70 68 


1300 


71 


70 68 


1400 


71 


71 68 


1500 


71 


72 68 


1600 


71 


72 68 


1700 


71 


74 69 


1800 


71 


74 


69 


1900 


71 


73 


69 


2000 


71 


72 


69 



The discharge temperature of the low pressure cylinders 
gradually increased and then remained stationary at 320 degrees 
Fahr. The intermediate cylinder discharge likewise attained 
a temperature of 292 degrees Fahr., and the high pressure 
cylinder, beginning at 375 lbs. per square inch, and at a tem- 
perature of 66 degrees Fahr., delivered from the intercoolers, 
gradually rose in temperature as the pressure increased, until 
it reached 2000 lbs., and after running at that pressure for one 
hour, the thermometer indicated its maximum, viz., 358 degrees 
Fahr. 

The sum total of those temperatures, viz., 970 degrees, as 
compared to the adiabatic temperature of single stage compres- 
sion to 2000 lbs., which is 1762 degrees Fahr., indicate the 
work saved by the three-stage method of compression combined 
with the jacket and ram cooling devices. 

The compression throughout the whole range was practi- 
cally regular, being as an average 115.1 lbs. for each 500 revolu- 
tions of both machines. 

The mean of many cards taken from the steam cylinders 
showed that each compressor absorbed 342.61 I. H. P., while 
the cards from the three air cylinders showed 293 78 I. H. P. 
for each compressor. The work then absorbed by the friction, 
inertia, etc., was 48.83 I. H. P. or 14.2 percent of the indicated 
power employed, showing a mechanical efficiency for the com- 
pressor of 85. S per cent, which is high, especially in view of 
the facts that the engines were new and consequently stiff to 
some extent, and also that some extra friction is developed at 
the ram stuffing-boxes as compared with a compressor working 
at the usual air pressures. 

The resisting load of 48.83 H. P. while the compressors 
were doing full duty may be compared with the friction load 
on the machine without air pressure, and an interesting result 



THE PNEUMATIC TORPEDO PLANT. 



151 



Fort Point 

Air Compressing Plant 

«= Steam *n Air Cards = 




152 THE PNEUMATIC TORPEDO PEANT. 

obtained. Cards taken showed that this friction load was 32.4 
H. P., being .663 of the resisting work under load and showing 
an increase of 50.7 per cent in the resistances between no load 
and full load. 

The combined indicator cards illustrated herewith are 
plotted from actual cards and show a saving of 36.8 over adia- 
batic single stage compression. 

The boilers for this plant were of the Return Tubular type, 
and manufactured by the Chandler & Taylor Co. of Indian- 
apolis, Ind.; were 72 inches in diameter, by 16 feet long, and 
of a nominal horse power of 500, which were increased by the 
forced draught employed, to about 750 horse. 

These boilers were tested to 150 lbs. to the square inch, and 
fully satisfied the requirements of the Treasury Department. 
The forced draught was employed because it was not con- 
sidered desirable to continue the stacks above the roof, and thus 
give an opportunity for invading forces to discover the posi- 
tion of the plant. A short stack was therefore necessary, 
about fifteen feet in length, which required the employment of 
a forced draught. The forced draught was instituted b}* two 
Sturtevant fans, with engines attached, having cylinders three 
inches in diameter by three and a half inch stroke. These fans 
delivered each 12,000 cubic feet per minute of free air, through 
a 22-inch main, which, passing underneath the battery of four 
boilers, was connected to each by a 10-inch outlet underneath 
the grate bars. It was found during the test that these fans 
need be run only to about 60 per cent of their capacity. 

The engines exhausted their steam into two heaters of 
the National type, of 300 H. P. each, which furnished to the 
boilers feed water at a temperature of 200 degrees Fahr. 

The Feed Pumps were of the Deane type, being Duplex and 
two in number, the steam cylinders being six inches, the 
water cylinders being four inches, and the stroke being six 
inches. At a slow piston speed these pumps furnished all the 
necessary water, which was drawn from the pits after being 
heated by the air from the compressors. 

As an auxiliary there are installed alongside of the Feed 
Pumps two Nathan Injectors of 300 H. P. each, which are 
amply sufficient to furnish all of the water necessary to feed 
the boilers. 

During the test for rapidity of firing, while the plant was 
supposed to be strained to its utmost, the firemen had ample 
time to observe the operation of the compressor plant, showing 
that the boilers were more than sufficient to supply the steam 
necessary for the proper operation of the compressors. 

The electrical plant was furnished by the Electrical En- 
gineering Company of this city, and consisted of one 35-kilo- 
Watt compound wound dynamo, capable of being worked up 
to 25 per cent of its rated capacity for thirty minutes without 
undue heat, and operated by an Armington & Sims engine. 

This dynamo was connected by about 800 feet of two-wire, 
insulated copper cable, encased in lead covering, and capable 



THE PNEUMATIC TORPEDO PLANT. 



153 




154 THE PNEUMATIC TORPEDO PI.ANT. 

of carrying a current of 400 amperes, without undue heating. 
This cable was placed in and fastened to the side of an 
underground conduit. 

This Company also placed in position, at about ten feet 
distant from the dynamo, a switchboard of slate, and wired 
complete, having three double-pole three hundred ampere 
knife switches. 

The compressed air, after leaving the compressors and 
being confined in the storage tanks, was distributed to the three 
guns independently, through a manifold of bronze, having 
attached five gauges, two registering 2coo lbs., and three 1250 
lbs., and so arranged with valves that any or all of the guns 
could be operated at once. 

This air is carried to the underground storage reservoirs of 
the guns, through a pipe having an outside diameter of 2]/ 2 
inches, and inside diameter of i)4 inches and duly tested to 
3500 lbs. to the square inch for tightness. 

From the guns to these manifolds also there are three cop- 
per pipes, % inch inside diameter by ]/ z inch outside diameter, 
to register the pressures at the manifolds that are contained in 
the carriages of the guns. 

This is in general the description of the air-compressing 
plant. We now come to speak of the guns themselves, which 
were manufactured at the West Point foundry on the Hudson, 
each 15 inches in diameter, with a length of 50 feet; each gun 
mounted on its carriage, weighing about 70 tons, perfectly bal- 
ances, and these are mounted upon concrete foundations. 

The tests of these guns for their mechanical efficiency, 
which may be called their ease of operation, showed that they 
could be traversed by the electric motors, which were situated 
in the gun carriage, in an average of one minute, throughout 
the entire 360 degrees, and they could be elevated from extreme 
elevation to extreme depression, in from eight to eleven 
seconds. Any one familiar with the length of time necessary 
to operate ordinary powder guns by hand will appreciate the 
fact that this facility of operation is marvelous. 

For testing these guns for mechanical efficiency, the 
requirements were, first, that 45 shots should be fired in the 
first hour and 30 shots in the hour succeeding. Inasmuch as 
the wastage of air would be the same whether actual projectiles 
were fired, or whether the air was simply wasted through the 
muzzle of the gun in "air shots," no projectiles were fired in 
this test, and it was found for the first hour that 45 shots were 
fired and the compressors running at their normal speed regis- 
tered a final pressure of 1800 lbs., it being thus demonstrated 
that the compressors were amply sufficient to maintain any 
requirements which might be placed upon the gun. Twenty 
air shots were fired to ascertain the utmost rapidity with which 



THE PNEUMATIC TORPEDO PLANT. 1 55 




35 K. W. Dynamo for ranging Dynamite Gun 



156 THE PNEUMATIC TORPEDO PLANT. 

they could be discharged, and the same were discharged in 7^ 
minutes, though the contract did not require that these shots 
should be discharged inside of 30 minutes, it being thus 
demonstrated that the compressors and the guns were amply- 
capable to maintain the test required by the Government. 

The test for rapidity of firing with actual projectiles took 
place next. The projectiles used were pieces of gas pipe 12 
inches in diameter and 8 feet long, loaded with sand. The 
weight was 1040 lbs. Each one of the three guns was required 
to fire five of these projectiles within twenty minutes. The 
test developed the fact that these projectiles were all discharged 
from each gun within eight and one-half minutes, and they 
were by far the most interesting feature of the whole test. 

Having no means for maintaining the accuracy of their 
flight, these projectiles were nevertheless thrown for the first 
one-half distance of their flight perfectly accurate; that is, they 
maintained the position of a well-directed projectile, after 
Which they tumbled end over end and fell into the sea. With- 
out any plain table measurements being taken upon them, they 
apparently fell quite accurately within a small target. 

The time of flight of these projectiles averaged about nine- 
teen seconds for about 2200 yards. 

The question of rapidity of firing and of loading having been 
determined, the next test was one of accuracy, and the live 
projectiles were discharged from these guns at a distance of 
5000 yards. The projectiles used were of the eight-inch cali- 
ber, the difference in diameter being made up by wooden pis- 
tons in four sections so that the wooden pieces would fly off 
after the projectile had left the gun, leaving it free to make its 
flight. The first projectile flew 5000 yards and exploded; the 
second projectile flew 5070 yards and exploded; the third pro- 
jectile flew 5015 yards and exploded; the fourth projectile 
flew 5040 yards and exploded; all of these projectiles being 
plotted on a plane table in a rectangle 70 yards long by 20 
yards wide, the time of flight being about 27^ seconds. 

As a matter of experiment, two shots were fired into the 
hills of Marin County, at a distance of 3350 yards, each with 
the 8-inch sub-caliber shell loaded with 100 lbs. of dynamite, the 
first shot being fired five days previous to the second shot. The 
shots struck within 45 yards of each other and exploded in a 
perfectly satisfactory manner; in fact, the pits caused by the 
explosion joined each other. The larger shells, viz., the 15- 
inch full caliber projectiles being eleven feet long and weighing 
some 1050 lbs., loaded with 500 lbs. of nitro-gelatine, were 
thrown into the sea at a range of an average of 2100 yards. 
They exploded practically upon striking the water, throwing 
into the air a column of water about 100 feet in diameter at the 



THE PNEUMATIC TORPEDO PI,ANT. 157 

base, and, from the levels taken at the gun, about 400 feet in 
altitude. 

The tests as above enumerated were perfectly satisfactory in 
every respect and exceeded in every way the requirements of 
the Government. There were no mistakes made and no delays 
whatever caused by the air-compressing plant or the gun plant, 
which probably exceeded the Government requirements in an 
aggregate of over one thousand per cent, if the various exceed 
percentages of the different tests were added together, and 
which reflected great credit upon the manufacturers of the 
power plant, the constructing engineer, the manufacturers of 
the guns and projectiles, and also the Pneumatic Torpedo & 
Construction Company of New York, which contracted for and 
thus successfully carried to completion their contract with the 
Government. 



I58 ROCK DRILLS. 



ROCK DRILLS. 



The RIX and the GIANT ROCK DRILLS are manufactured 
in San Francisco, Cal., and their construction is the result of a 
study of the requirements of the Pacific Coast in rock drilling, 
covering the last twenty years. It has been the aim of the man- 
ufacturers of these machines to produce something which will be 
especially satisfactory to the miners of the Pacific Coast. 

Many of the improvements in these machines have been 
suggested by the operators of the drills themselves, to suit par- 
ticular conditions, and it has been the aim of the manufacturers 
to construct a machine which is rapid and powerful in its 
action. 

The GIANT and the RIX DRILLS are manufactured under 
the following patents, controlled by EDWARD A. RIX. 

U. S. PATENTS AS FOLLOWS. 

Re-issue 0,705 Patent No. 190,699 

Patent No. 149,013 Patent No. 206,067 

Patent No. 152,712 Patent No. 235,296 

Patent No. 156,003 Patent No. 235,816 

Patent No. 169,389 Patent No. 255,335 

Patent No. 172,529 Patent No. 410,334 

Patent No. 178,214 Patent No. 454,228 
Patent No. 490,152 
Others pending. 



ROCK DRILLS. 



159 




i6q 



ROCK DRIUS. 




ROCK DRIW^. l6l 

Knowing that the average man who runs a rock drill is not 
a skilled mechanic, in the construction of tbe RIX DRILL the 
aim has been to produce a valve motion which could not by any 
means whatever go wrong or fail to go together, providing no 
piece should be omitted. To accomplish this the entire VALVE 
MOTION is arranged symmetrical to a line perpendicular to the 
line of motion and passing through the center of the exhaust. 
This permits the main valve spool, the caps, plates, and buf- 
fers, the auxiliary valve, the whole valve chest, or anything per- 
taining to it, to be reversed in any way, and the result is a 
proper and complete valve motion, and it also allows the ex- 
haust to be turned in any direction by simply using an ordinary 
street elbow. 

All JOINTS on either of these drills are scraped, and there 
are no gaskets to get out of order. 

One of the most annoying faults about imported rock drills 
is the rubber buffer, which has to be introduced into both heads 
in order to prevent accident to the heads by the careless opera- 
tors. Especially is this true when steam is used, for the rubber 
rapidly disintegrates and interferes with the proper working of 
the machine. In both the RIX and the GIANT DRILLS these 
interior buffers are dispensed with and a SPIRAL SPRING is 
placed on the back head of the machine which does service for 
both heads and which never wears out. In fact, a duplicate 
spring has never been furnished for any of these machines. A 
flat bow-spring does not accomplish the same result, as it breaks 
quite readily, and is generally replaced by a solid bar to avoid 
further difficulty. 

Quite a feature with the GIANT and RIX DRILLS is in the 
use of the same sized COLUMN, CLAMP, and TRIPOD for any 
of the machines. The result is that a mine need purchase but 
one sized mounting, and any drill will fit thereon. A 3-inch drill 
may be taken out of the heading if hard rock is encountered 
and a larger machine attached to the same clamp at once, 
without any re-setting of the column, and this is also found 
especially valuable in upraising work. 

All of the machines above the 2^-inch size use the same 
hose and the same COUPLINGS, and any of the machines will 
take drill steel of any size up to iX-inch, and use any shape 
bushing. 

The above-named conveniences are of great consideration, 
and have never failed to commend themselves to intelligent 
purchasers. It may be urged that a COLUMN which is large 
enough in diameter to properly carry a 3-inch machine is too 
small for a 3^ -inch drill. This may be true where the 
machines stand away from the column to any extent and 
where they are being racked by lost motion and where they 
reciprocate slowly, but with the GIANT and RIX machines, 
which hug the column closely and which have no lost motion on 
account of the DOUBLE FEED NUT DEVICE, and which 



l62 



ROCK DRII^S. 




Fig. 63.— RIX ROTATING DEVICE. Patented. 



ROCK DRILLS. J 63 

reciprocate fully fifteen percent faster than any other drill, it is 
not necessary, and therefore a purchaser need not pay for that 
which he does not require. 

The ROTATING MOTION in these drills is one of the finest 
features about them, and it fulfils perfectly every requirement. 
From the sketch, it will be seen that it consists of an internal 
ratchet engaging with swinging pawls carried in the head of 
the rotating bar. A very slight spring pressure serves to 
throw them into contact, when by the nature of the angles of 
adjustment the pawls will be carried into a pinch that cannot 
slip or be broken. All the angles in the ratchet and pawls are 
right angles ; therefore the ratchet may be reversed after it is 
worn on one side, and equal service be given to the other. 

The same is true of the PAWLS, and being symmetrical, it 
does not matter which side or end is first presented, for duty. 

This feature of having nearly all of the moving parts sym- 
metrical and reversible is quite a feature in the construction of 
these machines and is of immense assistance in the cost of 
operating and convenience, as well as being very useful in 
emergency. 

It is not necessary that these PAWLS SHOULD BE REVER- 
SIBLE, — a fact which has been taken advantage of by an East- 
ern drill manufacturer — and the owners of the patent on this 
rotating device desire us to state for them and in their behalf 
that the INTRODUCTION OF THIS SWINGING PAWL IN 
A DRILL ROTATING MOTION, WHERE THE PAWL IS 
SYMMETRICAL OR NON-SYMMETRICAL, IS AN IN- 
FRINGEMENT UPON THEIR RIGHTS, AND ANY PAR- 
TIES USING SAME WITHOUT PROPER LICENSE FROM 
THESE ORIGINAL PATENTEES WILL BE ENJOINED 
FROM USING SAME AND BE ALSO REQUIRED TO PAY 
DAMAGES. 

All rock drills, of either the RIX or the GIANT pattern, 
which use compressed air as a motive power, are supplied with a 
FRONT HEAD, which has no stuffing box but which is inter- 
nally packed with a leather-cupped ring, which is absolutely per- 
fect in its action. This is an old method of packing a drill piston 
rod, having been used about twenty years ago, and is now used 
by other drill makers occasionally. It has, however, never 
given any great amount of satisfaction and never was absolutely 
tight, for the air had always escaped through the split in the 
ring, and the cup was not the proper shape. 

The LEATHER CUPS, however, for these drills are made 
by a machine especially constructed to shape the joints, form- 
ing a perfect interior and exterior cylinder, one-eighth of an 
inch apart. There is no split at all, and they remain perfectly 
tight under any pressure and last about four months under 
continuous wear. 



]64 



ROCK DRILLS. 



#*. 




ROCK DRII^S. 



I6 5 




Fig. 65.— GIANT DRILL, Mounted 011 Tripod. 



l66 ROCK DRII^S. 

The FEED NUT DEVICE is another special feature of both 
of these machines. All other rock drills are provided with a 
single feed nut, and this together with the feed screw naturally 
wears rapidly. After wearing so that the lost motion becomes 
apparent, it acts materially against the cutting power of the 
machine, as well as being noisy and a fruitful source of acci- 
dents, for at every stroke of the ordinary rock drill it thumps 
back and forth in its cage to the full extent of this lost motion. 
The only remedy is a new nut and screw. 

In the RIX and GIANT DRILLS, by means of the double 
feed nut all trouble of this kind is avoided. One of the nuts 
is secured to the cylinder of the drill in a manner similar to all 
drills; the other has a toothed edge and may be turned to the 
extent of a tooth at a time as the feed screw wears. This 
allows the front edge of the feed screw thread to work on the 
back edge of the first feed nut thread, and the back edge of 
the feed screw thread to work on the front edge of the second 
feed nut thread, thus furnishing the feed screw with practically 
one perfect-fitting nut all the time, and in this manner, a feed 
screw may be worn until its threads break away without any 
lost motion being apparent in the drill. It needs no comment 
to show that the drill uses FEW FEED SCREWS, in fact, the 
life of the screw is not less than TWO YEARS in any case, 
barring accident. 

The clamp is a powerful one, very light, a perfect DROP 
STEEL FORGING, and has but ONE BOLT, so that it is easy 
to work, and being very light can be operated in half the time 
that it requires for some others. This clamp has been in con- 
tinuous use for twenty years and has proved itself to be 
thoroughly reliable. 

The PISTON of both the RIX and the GIANT DRILLS is so 
arranged that it will receive any size bushing up to ij^ inches. 
The drills are always fitted with an octagon bushing, unless 
otherwise ordered, for that style receives the steel just as it is 
manufactured and thus saves the expense of TURNING THE 
SHANKS as well as doing away with the annoying breakage 
which happens when the ends of the steel are turned. The full 
size octagon is none too strong to withstand the powerful blows 
delivered by these machines and a much lower pressure must 
be used if the drill shanks are turned. 

The COLUMN MOUNTINGS used for these machines are 
similar to those used by other makers, excepting that only one 
size is manufactured. Other sizes are made and kept in stock to 
satisfy the ideas of customers who have been used to other 
drills, but the increased size is not necessary to a satisfactory 
working of the machines. 

The TRIPOD is one furnished with universal joints to its 



ROCK DRT1XS. 167 




Fig. 66.— 23^ -inch RIX DRIIyl, Mounted on Tripod. 



l68 ROCK DRIU,S. 

legs and has stood the test of twenty years of good service. A 
clamp is always used with this tripod; this enables the head of 
the tripod to be used as a short column, so that the drill may 
be given a lateral motion of about four inches, a feature which 
is very useful in drilling holes in uneven rock full of cracks or 
fissures, or which from any cause deflects the drill steel. 

In the RIX DRILL the VALVE MOTION is in every way 
superior to anything which now operates a rock drill, and one 
of the most noticeable things about the drill when it is running 
alongside of other makes, is the wonderful regularity of its 
motion reciprocating as evenly as a steam engine, and deliver- 
ing a blow with much greater velocity than any other machine, 
and also more of them. Most of the drill makers make a claim 
for an uncushioned blow, and that the valve does not change 
until after the blow is struck, but these are not facts which are 
consistent with another claim which they make; viz., that 
their machines are the only ones which make a variable stroke. 
None of the standard makers claim that the reversing of the 
valve is dependent upon the striking of the rock, yet their 
statements would lead one to that conclusion. Every one 
knows that the drills will run at quite a speed without striking 
even the front head, and any one who examines their valve 
mechanism will perceive that it is practically the same for both 
the front and back stroke, and they certainly would not like 
the inference drawn that the piston must strike the back head 
in order to reverse the valve. 

The fact is that all the standard drills strike a cushioned 
blow, and the valve is always reversed before the drill strikes 
the rock, and this must necessarily be so in order to allow for 
a variable stroke, and to provide for a sufficient number of 
strokes. Drills have been used in Europe, and many experi- 
mental ones made here have been so constructed that the valve 
changed after the blow was struck. This, undoubtedly, gives 
the heaviest blow, but the number of the strokes is so limited 
that can be delivered in a minute, that the machine could not 
begin to do the work an ordinary rock drill can do. The 
more the cushion in a drill, the faster it will reciprocate, and 
the less effective will be the blow. The less the cushion, the 
heavier the blow and the less the number of strokes. The 
shorter the working stroke, the greater the number of strokes 
and the less the blow, and the less the working pressure, the 
less the number of strokes and the less the force of the blow. 
Therefore, in fashioning a rock drill, the result must be a 
mean between these four relations, which shall give the best 
results. In other words, the length of stroke, the amount of 
cushion, the number of strokes, and the pressure used, must be 
so adjusted with relation to each other that the best result-will 
be produced — allowing, of course, that the diameter of the 
cylinder has been determined. All these problems have been 
very satisfactorily solved in both the RIX and the GIANT 
machines. 



ROCK DRIIyl^S. 169 

The VALVE MOTION of the GIANT DRILL is one which is 
operated directly from the piston by mechanical contact, and 
this drill is manufactured to satisfy the beliefs of some drill 
users that a machine of this construction is better than a ma- 
chine operating with the auxiliary valve motion, such as the 
RIX. 

The sizes of the GIANT DRILL are made to alternate with 
the sizes of the RIX, so that the following Tables of sizes and 
capacities, which represent a complete range, are offered to 
the public: 



170 



ROCK DRIIJ,S. 























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172 ROCK DRILLS. 

DUPLICATE PARTS OF THE RIX 
ROCK DRILLS. 



i — Rotating Nut. 

2 — Piston, bare. 

3 — Piston Ring. 
4-5 — Sleeve. 

6 — Feed Nut (adjustable). 

7 — Feed Nut (plain). 

8— Yoke for Feed Nuts. 

9 — Lower Head. 

10 — Leather Crimp for Lower Head, 
ir — Chuck Bolts and Nuts. 
12 — Chuck Bushing. 
13 — Chuck Key. 
14 — Steam Chest, bare. 
15 — Main Valve. 
16 — Steam Chest Cap. 
17— Steel Cushion Plate. 
18 — Rubber Cushion. 
19 — Auxiliary Valve. 
20 — Auxiliary Valve Spring. 
21 — Auxiliary Valve Claw. 
22 — Oil Screw. 
23— Yoke for Head Bolts. 
24 — Head Spring. 
25 — Cover for Ratchet Ring. 
26 — Bottom Plate for Ratchet Ring. 
27 — Rotating Bar. 
28 — Cylinder, bare. 
29— Guide Block. 
30— Shell Strip. 
31 — Cylinder Bolts. 
32— Shell Bolt. 
33 — Feed Screw. 
34— Yoke for Shell Bolts. 
35 — Feed Screw Handle (brass). 
36 — Pawl. 
37 — Ratchet Ring. 
38 — Pawl Spring. 
39 — Shell without Strips or Yoke. 
40 — Clamp Wrench. 
41— Steam Chest Wrench. 
42 — Chuck Wrench. 



ROCK DRILLS. 



173 




DUPLICATE PARTS OF THF, R1X ROCK DRILL. 



ROCK DRILLS. 




duplicate; parts of the giant DRir.r y . 




ROCK DRII^S. 175 

DUPLICATE PARTS OF THE GIANT 
ROCK DRILLS. 

1 — Rotating Nut. 

2 — Piston, bare. 

3 — Piston Ring. 

4 — Valve Chest. 

5 — Valve Chest Cover. 

6 — Feed Nut (adjustable). 

7 — Feed Nut (plain). 

S— Yoke for Feed Nuts. 

9 — Lower Head. 

10 — Leather Crimp for Lower Head. 
11 — Chuck Bolts and Nuts. 
12 — Chuck Bushing. 
13 — Chuck Key. 
14 — Valve. 
15 — Valve Rocker. 
16 — Piston Ring Spring. 
17 — Rocker Pin. 
22 — Oil Screw. 
23 — Yoke for Head Bolts. 
24 — Head Spring. 
25 — Cover for Ratchet Ring. 
26— Bottom Plate for Ratchet Ring. 
27 — Rotating Bar. * 

28 — Cylinder, bare. 
30— Shell Strip. 
31 — Cylinder Bolts. 
32— Shell Bolt. 
33 — Feed Screw, 
34— Yoke for Shell Bolts. 
35 — Feed Screw Handle (brass). 
36 — Pawl. 
37 — Ratchet Ring. 
38— Pawl Ring. 

39 — Shell without Strips or Yoke. 
40 — Clamp Wrench. 
41 — Steam Chest Wrench. 
42 — Chuck Wrench. 



176 ROCK DRILLS. 



RIX PLUG AND FEATHER DRILL. 

The Rix Plug and Feather Drill, a cut of which appears in 
Fig. 66^, is the smallest drill manufactured by this Company. 
It has a two-inch diameter cylinder, from four to five inch 
stroke, and makes from seven hundred to nine hundred strokes 
per minute. It is designed for drilling small holes about one 
inch in diameter and for depths up to twenty-four inches. 

For quarry work it is mounted on a tripod, as shown in the 
cut, and for mining purposes it has the usual column mountings. 
The tripod is one which gives a wide range of movement. 

The Drill itself weighs about 65 lbs. and is extremely con- 
venient to handle. It is generally used with seven-inch steel 
and the chuck is made tapering to take the end of the steel in 
similar to the way a twist drill fits in its socket. This will be 
found most convenient in the handling of these small drills. 

This machine will tfe found very handy for many ranges of 
work, including the driving of wooden pins in caison, scow, or 
dry dock constructions where the pins have to be driven from 
underneath the work being constructed. 

In the use of air it is very economical, taking about twenty- 
five cubic feet of free air per minute. 



ROCK DRILLS. 



177 




u 




Fig. 65y 2 — RIX PLUG AND FEATHER DRII,!,. 



A FEW GENERAL HINTS. 

Buy a Compressor larger than you need. 
Buy one which is economical. 
Run it slow. 

Put in good foundations. 
Have a spare boiler if you can afford it. 
Have a clean, ship-shape engine-room. 
Cover all of your steam-pipes. ' 
Provide large air-pipes. 

A generous sized receiver will come in handy. 
Make as few short turns as possible in the air-pipe. 
Use a good cylinder lubricant. 
Circulate ample water in the air cylinder jackets. 
Have some extra compressor valves, and change them fre- 
quently. 
Put in one or two shut-off valves in your air-pipe. 
Keep the receiver properly drained. 
Buy a rock drill of a size best suited to the work, and don't buy 

any unless your mind is made up to do it properly. 
Have plenty of steel, so your men are not running for drill-bits 

all the time. 
Get a good blacksmith, and have him keep both ends of the 

steel properly sized. 
Drill good-sized holes, for the powder does better work at 

the bottom of a hole. 
Have an intelligent workman to run the drill. 
Have an extra drill always ready in the shop, and you will find 

less breakages and accidents occur to those in use. 
Oil the machine well before starting. 
See that all the nuts are tight. 
Be sure that no dirt is in the hose before it is attached to the 

machine. 
Keep the column well jacked up, and have blocks of wood top 

and bottom. 
Start the holes on the shortest stroke of the machine, and 

gradually lengthen out the stroke as the hole deepens. 
Feed the machine so that the piston will clear the front head. 



A FKW GENERAI, HINTS. 179 

In soft ground, make haste slowly. 

If the steel gets stuck in the hole, strike it sharply until it 
releases. 

Never strike the chuck. 

Do not screw up too hard on the chuck-nuts or clamp-bolts, 
for it is perfectly possible to break them. 

Keep your bushings in good order. 

A bit of cast-iron or iron borings thrown into a fissured hole 
will help it out. 

A piece of broken drill-bit will often cause a hole to run out. 

Drill wet holes whenever you cau. 

A leaky stuffing-box will often prevent the piston pulling out 
from a tight hole. 

Never run the drill against the head to throw the steel out. 

Do not expect the drill to furnish brains to run itself. 

Do not expect it to run without repairs. 

Carry as high a pressure as possible when your rock is hard, 
and calculate always that the repairs will vary, as the pres- 
sure and also the work done. 

Remember that a rock drill is an engine, after all, and the 
fewer times it goes over the dump, or is dropped off the 
column, or is blasted upon, the longer it will last. 

Generous and faithful oiling will help a machine wonderfully. 

Use a good steam-trap when using a drill in a quarry. 

A tripod must be securely set to do good work. 

The same kind of drill-points do not work equally well in 
different kinds of rock. 



i8o 



ROCK DRILLS. 




Fig. 67.— Column with Arm 



Fig. 68.— Plain Column. 



Column Mountings for Rock Drills. Made in any length. One price for 
all lengths under ten feet. 



ROCK DRII^S. 



181 




AIR RECEIVERS. 

In conjunction with an air compressor there is generally- 
attached a reservoir called an air receiver. The purpose of this 
is twofold: to collect the moisture which is condensed from the 
air after it is compressed, and also to afford a sufficient volume 
to receive the intermittent discharges from the compressor, and 
reduce them to a continuous flow in the pipes leading from the 
receiver. 

The ordinary receiver is fitted with an air gauge, a safety 
valve, and a valve to draw off the moisture. These are arranged 
as shown in the cut herewith attached. 

Our reservoirs are made of homogeneous steel, with bumped 
heads, of a sufficient thickness to be tight at 125 lbs. cold 
water pressure, for all ordinary plants. We prefer bumped 
heads because bracers are not then necessary. We put three 
cast iron feet on one end of the receiver for it to stand upon, 
and sufficiently high to permit drawing off the entrained water 
water easily, above the floor line. 

We are frequently asked where is the proper place for 
the receiver — at the compressor or in the mine ? We reply, 
both. There never was too much receiver capacity on any 
plant. We do not believe it essential to have a very large 
receiver near the compressor, providing there is an oppor- 
tunity to place one further along the pipe. About fifteen 
times the cylinder capacity would, in all ordinary cases, keep 
the gauge steady at the compressor. It would be a great 
benefit to systems having medium or small size pipes to 
have as large a receiver capacity at or near the point where 
the air is used, and especially is this the case where hoisting 
engines are drawing from the air pipes. It requires no engi- 
neering knowledge to see that if air receivers could be made 
large enough to diffuse the intermittent work into an average 
draw on the pipe leading from the compressor, that the com 
pressor need be only large enough for the average work, whereas 
ordinarily it must be large enough for the maximum work, and 
consequently uneconomical. 

It is not generally practicable to have reservoirs so large, 
however, but a reasonable approach can be made to this capa- 
city without much expense. We have known compressors to 
do 25 per cent more useful work by putting receivers near the 
point where the air is to be used, and where numerous bends 
and elbows are required in the main pipe. 

When air is drawn too fast through the main pipe, causing 
a reduction, of pressure, the increase of volume due to the loss 
pressure causes quite a marked increase in all the frictional 
losses through the system. We therefore advise receivers at 
both ends of the line, the smaller ones near the compressor, and 
this is independent of the amount of storage capacity in 
the pipe. 



AIR RECEIVERS. 



DIMENSIONS OF AIR RECEIVERS. 

Diameter, inches 30 30 36 36 36 42 

Height, feet 6 8 8 io 12 8 

Thickness of Shell, inches . }( % % % % }( 

Thickness of Heads, inches. Xe s At Y& Y% % % 

« 

Weight 700 900 1200 1400 1600 1800 

No. of 3>(-i n ch Drills Re- 
ceiver is suitable for 11 2 3 4 5 

Diameter, inches 42 42 42 48 48 48 

Height, feet 10 12 16 10 12 j6 

Thickness of Shell, inches. % % % y it s / lt c / t 

Thickness of Heads, inches Y& Y& Ys yU %e Yit 

Weight 1900 2000 2100 2400 2900 3400 

No. of 3X-inch Drills Re- 
ceiver is Suitable for S 10 12 12 15 20 



AIR RECEIVERS. 




toxccooooooo oooo o o c 



(puroooooooo o o qoooooooooooqcchu 



<mmxoooooooooo oooooooooocaJS 



ooo ooo ooooooooc 




Verticav. a»r Receiver 



AIR RECEIVERS. 



I8 5 




i86 



DRILL BITS AND HOSK COUPLINGS. 



SPECIAL BLACKSMITH TOOLS FOR 
DRILL BITS. 

Fig. 72. Fig. 73- Kg- 74- Fig. 75- Fig- I 6 - 




Sow. Dolly. Spreader. Flatter. Swedge. 

RIX PATENT HOSE COUPLINGS- 



This coupling 
is the only coup- 
ling which will 
stay on a hose 
under all condi- 
tions of use. They 
have been used 
successfully at 600 
lbs. per square 
inch, and are per- 
fectly reliable. 
The nature of the 
coupling is such 





Fig- 77- 

that it is rigidly 
connected to the 
hose, and nothing 
but the tearing away 
of the hose itself 
will separate it from 
the coupling. 



Fig. 78. 



SIZES AS FOLLOWS: 

For i-inch 4 or 5 ply Hose. 
For 3^-inch 4 or 5 ply Hose. 
For 2-inch 4 or 5 ply Hose. 



LUBRICATORS AND LUBRICANTS. 187 



LUBRICATORS AND LUBRICANTS. 

All of our Compressors for ordinary pressures, that is, up to 
200 lbs. per square inch, are provided with the Ellis Sight 
Feed Lubricator for the air cylinders. This, or some similar 
device, is the only method for certain and economical lubrica- 
tion. The ordinary oil cup delivers its entire contents in a 
short time, and there is no means of knowing when it requires 
filling, except by opening it. For all of our crank pins we use 
the Economy Oiler, which feeds only when the compressor is 
running. We have reports stating that one filling of one of 
these 4^2-ounce oilers on the crank of a 10-inch compressor 
lasted four weeks of continuous run. 

The ordinary cylinder lubricating oils will not suffice for 
single stage dry compressor cylinders, where the compression 
is almost adiabatic from 200 degrees to 400 degrees, depending 
on the pressures. Poor oils are decomposed at these tempera- 
tures, and form combustible gases which may explode with 
dangerous effect. There was an explosion of this kind in the 
Idaho Mine, Grass Valley, a number of years ago, which 
destroyed several hundred feet of 6-inch air pipe in the shaft. 
Oils of at least 600 degrees fire test should be used. Any oil 
which burns on the outlet valves, leaving a hard, black, 
rubber-like substance, is not fit to be used. 

Some engineers mix kerosene or coal oil with their cylinder 
lubricant, to cut the deposit and dirt from their valves, but it 
is a dangerous practise and will lead to accident, because the 
fire test of coal oil does not ordinarily exceed 175 degrees Fahr. 

We carry in stock special oils for Compressors and Rock 
Drills, known as 

RIX COMPRESSOR OIL. 

RIX ROCK DRILL, OIL- 



l88 AIR CYLINDER OIL CUP. 



ELLIS AIR CYLINDER OIL CUP. 

The cylinders of Air Compressors are generally lubricated 
with a plain oil cup, and a great deal of difficulty is encoun- 
tered in making this feed steady enough for practical purposes. 
Hither the cup will not feed at all, or it will feed its entire 
contents in a few minutes. The 
lubricator which we are offer- 
ing is a special lubricator, de- 
signed so that the pressure of 
air in the cylinder will force the 
oil through a small opening, 
which may be regulated, into 
the cylinder. The drops may 
be regulated as slow or as fast 
as necessary, and are made to 
drop in plain view, so as to 
make it a drop sight lubricator, 
something entirely new for air 
compressing cylinders and 
which we feel sure will be a 
great relief and satisfaction to 
^' '9- those who have plants equipped 

with this class of machinery. It goes without saying that a 
lubricator of this kind will use about one-half of the oil that the 
ordinary lubricators require. 

Made in either brass or nickel-plated finish, in the follow- 
ing sizes: j^-pint, ^-pint, ^-pint, i-pint, i-quart. 




APPENDIX. 



USEFUL TABLES, 

TO BE USED IN THE CALCULATION OF 

COMPRESSED AIR PROBLEMS. 



The following tables and data in general will be found 
useful in the calculation of Compressed Air Problems. These 
tables have been taken from Kent's Hand Book, from The 
Pelton Water Wheel Company's catalogue, and from Carnegie 
Phipps & Co.'s catalogue, and we desire to express to the 
publishers of these volumes our thanks. 



USEFUL TABLES. 

CIRCUMFERENCES AND AREAS OF CIRCLES 

Advancing by Eighths. 



191 



Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


1/64 


.04909 


.00019 


2 % 


7 4613 


4.4301 


G % 


19.242 


29.465 


1/32 


.09818 


.00077 


7/16 


7.6576 


4.6064 


y 4 


19.6:35 


30.680 


3/64 


.14726 


.00173 


14 


7.8540 


4.9087 


20.028 


31.919 


1/16 


.19635 


.00307 


9/16 


8.0503 


5.1572 


8 


20.420 


33.183 


3/32 


.29452 


.00690 


% 


8.2467 


5.4119 


20.813 


34.472 


5/32 


.39270 


.01227 


11/16 


8.4430 


5.0727 


8 


21 206 


35 785 


.49087 


.01917 


H 


8.6394 


5.9396 


21.598 


37. 122 


3/16 


.58905 


.02761 


13/16 


8.8357 


6.2126 


7. 


21.991 


38.485 


7/32 


.C8722 


.03758 


% 


9.0321 


6.4918 


% 


22.384 


39.871 








15/16 


9.2284 


6.7771 


8 


22.776 


41.282 


H 


.78540 


.01909 








23.169 


42.718 


9/32 


.88357 


.06213 


3. 


9.4248 


7.0686 


H 


23.562 


44.179 


5/16 


.98175 


.07670 


1/16 


9 6211 


7.3662 


% 


23.955 


45.664 


11/32 


1.0799 


.09281 


% 


9.8175 


7.6699 


8 


24.347 


47.173 


% 


1.1781 


.11045 


3/16 


10.014 


7.9798 


24.740 


48.707 


13/32 


1.2763 


.12962 


Ya 


10.210 


8.2958 


8. 


25.133 


50.265 


7/16 


1.3744 


.15033 


5/16 


10.407- 


8.6179 


% 


25.525 


51.849 


15/32 


1.4726 


. 17257 


% 


10.603 


8.9462 


k 


25.918 


53.456 








7/16 


10.799 


9.2806 




26.311 


55.088 


H 


1 5708 


.19635 


¥1 


10.996 


9.6211 


i£ 


26.704^ 


56.745 


17/32 


1.6690 


.22166 


9/16 


11.192 


9:9678 


§8 


27.096 


58.426 


9/16 


1.7671 


.24850 


% 


11.388 


10.321 


§ 


27.489 


60.132 


19/32 


1-.8653 


.27688 


11/16 


11.585 


10.680 


27.882 


61.862 


21/32 


1.9635 


.30680 


¥x 


11.781 


11.045 


9. 


28.274 


63.617 


2.0617 


.33824- 


13/16 


11.977 


11.416 


H 


28.667 


65.397 


11/16 


2.1598 


.37122 


% 


12.174 


11.793 


& 


29.060 


67.201 


23/32 


2.2580 


.40574 


15/16 


12.370 


12.177 




29.452 


69.029 








4. 


12.566 


12.566 


t<g 


20.845 


70.882 


H 
.25/32 


2.3562 


.44179 


1/16 


12.763 
12.959 


12.962 


rk 


. 30.238 


72.760 


2.4544 


.47937 


% 


13.364 


% 


30.631 


74.662 


13/16 


2.5525 


.51849 


3/16 


13.155 


13.772 


vk 


31.023 


76.589 


27/32 


2.6507 


.55914 


M 


13.352 


14.186 


10. 


31.416 


78.540 


% 


2.7489 


.60132 


5/16 


13.548 


14,607 


ft 


31.809 


80.516 


20/32 


2.8471 


.64504 


% 


13.744 


15.033 


32.201 


82.516 


15/16 


2.9452 


.69029 


7/16 


13.941 


15.466 


% 


32.594 


84.541 


31/32 


3.0434 


.73708 


H 


14.137 


15.904 




32.987 


86.590 








9/16 


14.334 


16.349 


% 


33.379 


88.664 


1- 


3.1416 


.7854 


% 


14.530 


16.800 


8 


33.772 


90.763 


1/16 


3.3379 


.8866 


11/16 


14.726 


17.257 


34.165 


92.886 


H 


3.5343 


.9940 


¥4 


14.923 


17.728 


11. 


34.558 


95.033 


3/16 


3.7306 


1.1075 


13/16 


15.119 


18.190 


% 


34.950 


97.205 


H 


3.9270 


1.2272 


% 


15.315 


18.665 


H 


35.343 


99.402 


5/16 


4.1233 


1.3530 


15/16 


15 512 


19.147 


% 


35.736 


101.62 


% 


4.3197 


1.4849 


5. 


15.708 


19.635 


VH 


36.128 


103.87 


7/16 


4.5160 


1.6230 


1/16 


15.904 


20.129 


8 


36.521 


106.14 


Vi 


4.7124 


1.7671 


% 


16.101 


20.629 


36.914 


108.43 


9/16 


4.9087 


1.9175 


3/16 


16.297 


21.135 


% 


37.306 


110.75 


% 


5.1051 


2.0739 


M 


10.. 493 


21 648 


12. 


37.699 


113.10 


11/16 


5.3014 


2.2365 


5/16 


16.690 


22.166 


% 


38.092 


115.47 


■H 


5.4978 


2.4053 


% 


16.886 


22.691 


H 


• 38.485 


117.86 


13/16 


5.6941 


2.5802 


7/16 


17.082 


23.221 


% 


38.877 


120.28 


% 


5.8905 


2.7612 


}4 


17.279 


23.758 




39.270 


122.72 


15/16 


6.0868 


2.9483 


9/16 


17.475 


24.301 


vk 


39.663 


125.19 








% 


17.671 


24.850 


8 


40.055 


127.68 


2. 


6.2832 


3.1416 


11/16 


17.868 


25.406 


40.448 


130.19 


1/16 


6.4795 


3.3410 


u 


18.064 


25.967 


13 


40.841 


132.73 


k 


6.6759 


3.5466 


13-16 


18.261 


26.535 




41.233 


135.30 


3/16 


6.8722 


3.7583 


% 


18.457 


27.109 


M 


41.626 


137.89 


l A 


7.0686 


3.9761 


15-16 


18.653 


27.688 


% 


42.019 


140.50 


.5/16 


7.2649 


4.2000 


e 


18.850 


28.274 


M&i 


. 42.412 


143.14 



192 



USEFUL TABLES. 



Diam. 


Circum . 


Area. 


Diam. 


Circum. 


Area.. 


Diam 


Cireum. 


Area. 


1 


42.804 


145.80 


21% 


68.722 


375.83 


30% 


94.640 


712.76 


43.197 


148 49 


32 


69.115. 


380.13 




95.083 


718.69 


43.590 


151.20 


H 


69.508 


384 46 


78 


95.426 


724 64 


14. 


43.982 


153.94 


S 


69.900 


388.82 


\& 


95.819 


730.62 


1^ 


44.375 


156 70 


70.293 


393.20 


78 


96.211 


736.62 


J4 


44.768 


159.48 




70.686 


397.61 


% 


96.604 


742.64 


% 


45.160 


162.30 


% 


71.079 


402.04 


vi 


96.997 


74869 


% 


45.553 


165.13 


1 


71 471 


406.49 


31. 


97.389 


754.77 


78 


45.946 


167.99 


71.864 


410.97 


% 


97.782 


760.87 


% 


46.338 


170.87 


28. 


72.257 


415 48 


jl 


98.175 


766 99 


46.731 


173.78 


^ 


72.649 


420.00 


H 


98.567 


773.14 


15 


47.124 


176 71 


H 


73 042 


424.56 




98.960 


779.31 


1 


47.517 


179.67 




73.435 


429.13 


7& 


99.353 


785 51 


47.909 


182.65 


Lg 


73.827 


433.74 


% 


99.746 


791 73 




48.302 


185.66 


% 


74.220 


438.36 


% 


100.138 


797 98 


MB 


48.695 


188.69 


% 


74.613 


443.01 


32 


100,531 


804 25 


% 


49.087 


191.75 


% 


75.006 


447 69 


ri 


100.924 


$.0.54 


8 


49.480 


194.83 


24 


75 398 


452.39 


k 


101.316 


816.86 


49.873 


197.93 


% 


75.791 


457.11 




101 709 


823.21 


16 


50.265 


201.06 


» 


76.184 


46186 


14 


102.102 


829.58 


& 


50.658 


204.22 


76.576 


466 64 


7B 


102.494 


835.97 


g 


51.051 


207.39 




76.969 


471.44 


l 


102.887 


842.39 




51.444 


210.60 


7» 


77.362 


476 26 


108.280 


848.83 


L£ 


51.836 


213.82 


% 


77 754 


481.11 


33 


103 673 


855.30 


7& 


52.229 


217.08 


78.147 


485.98 


% 


104.065 


861.79 


n 


52.622 


220.35 


26. 


78.540 


490.87 


I 


104.458 


868.31 


53.014 


223.65 


7& 


78.933 


495 79 




104.851 


874.85 


17 


53.407 


226.98 


54 


79.325 


500.74 


Ms 


105.243 


881.41 


^ 


53.800 


230.33 


9s 


79.718 


505 71 


% 


105 636 


88800 


*4 


54.192 


233.71 


Yi 


80.111 


510.71 


H 


106,029 


894.62 


% 


54.585 


237.10 


7& 


80503 


515.72 


% 


106.421 


901.26 


H 


54.978 


24053 


8 


80 896 


520.77 


34 


106.814 


907.92 


55.371 


243.98 


81.289 


525.84 


I 


107.207 


914.61 


s 


55.763 


247.45 


26. 


81.681 


530.93 


107.600 


921.32 


56.156 


250.95 


I 


82.074 


536.05 




107.992 


928.06 


18. 


56.549 


254.47 


82 467 


541.19 


L£ 


108 385 


934.82 


i 


56.941 


258.02 




82.860 


546 35 


7ft 


108.778 


941.61 


57.334 


261.59 


L£ 


83.252 


551 55 


8 


109.170 


948.42 


57.727 


265.18 


78 


88.645 


556.76 


109.563 


955.25 


» 


58. 119 


268.80 


3£ 


84.038 


562 00 


35 


109.956 


962.11 


58.512 


272.45 


v\ 


84.430 


567.27 


vi 


110.348 


969.00 




58.905 


276.12 


27. 


84.823 


572 56 


1 


110.741 


975.91 


59.298 


279.81 


vi 


85.216 


577.87 


111.134 


982.84 


19 


59.690 


283.53 


8 


85.608 


583.21 




111.527 


989 80 


V6 


60 083 


28727 




86 001 


588 57 


76 


111.919 


996 78 


^ 


60.476 


291 .04 


v2 


86.394 


593.96 


7& 


112.312 


1003 8 




60.868 


294.83 


78 


86 786 


599.37 


% 


112.705 


1010 8 


\& 


61.261 


298.65 


8 


87.179 


604.81 


36 


113.097 


1017 9 


§6 


61.654 


302.49 


87.572 


610.27 


7& 


113.490 


1025 


§ 


62.046 


306.85 


28 


87.965 


615.75 


I 


113 883 


1032.1 


62.439 


310.24 


% 


88.357 


62126 




114.275 


1039 2 


20 


62.832 


814.16 


H, 


88.750 


626.80 


!Uj 


114.668 


1046 3 


^ 


63.225 


318.10 




89.143 


532.36 


§6 


115.061 


1053.5 


» 


63.617 


322.06 


% 


89 535 


537.94 


8 


115.454 


1060 7 


64.010 


326.05 


vk 


89.928 


543 55 


115.846 


1068.0 


^6 


64.403 


330.06 


% 


90.321 


549 18 


37 


116 239 


1075 2 


% 


64.795 


334 10 


% 


90'713 


354.84 


% 


116.632 


1082 5 


f^ 


65.188 


338 16 


29 


91 106 


560 52 


8 


117 024 


1089.8 


».** 


65.581 


342 25 


H 


91.499 


566 23 


117 417 


1097 1 


21. 


65.973 


346 36 


8 


91 892 


571 96 




117 810 


1104 5 


^ 


66.366 


350.50 




92.284 


377 71 


78 


118 202 


1111.8 


| 


66.759 


354.66 


L£ 


92 677 


383.49 


8 


118.596 


1119.8 


67.152 


358.84 


5,| 


93,070 689.30 


118.988 


1126.7 


\4& 


67.544 


363 05 


s 


93 462 695 IS 


38 


119.381 


1134.1 


96 


67.987 


367 28 


98 855 700 98 


14 


119 773 


141.6 


% 


68.330 


371 54 


30 


94 248 1 


roe 86 


v± 


120, 166 


149.1 



TTSKFUIy TABLES. 



193 



Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


38 & 


120.559 


1156.6 


46^ 


146.477 


1707.4 


54% 


172.395 


2365.0 


<Hs 


120.951 


1164.2 


s 


146.869 


1716.5 


55. 


172.788 


2375.8 


7& 


121.344 


1171.7 


147.262 


1725.7 


% 


173.180 


2386.6 


3£ 


121.737 


1179.3 


47. 


147.655 


1734.9 


H 


173.573 


2397.5 


vk 


122.129 


1186.9 


H 


148.048 


1744.2 


% 


173.966 


2408.3 


39. 


122.522 


1194.6 


% 


148.440 


1753.5 




174.358 


2419.2 


1 


122.915 


"1202.3 


148.833 


1762.7 


% 


174.751 


2430.1 


12:5.308 


1210.0 


1 


149.226 


1772.1 


M 


175.144 


2441.1 




123.700 


1217.7 


149.618 


1781.4 


% 


175.536 


2452.0 


/^ 


124.093 


1225^4 




150.011 


1790.8 


56. 


175.929 


2463.0 


% 


124.486 


1233.2 


% 


150.404 


1800.1 


% 


176.322 


2474.0 


» 


124.878 


1241.0 


48. 


150.796 


1809.6 


H 


176.715 


2485.0 


% 


125.271 


1248.8 


% 


151.189 


1819.0 




177.107 


2496.1 


40. 


125.664 


1256.6 


1 


151.582 


1828.5 


14 


177.500 


2507.2 


% 


126.056 


1264.5 


151.975 


1837.9 


7& 


177.893 


2518.3 


y± 


126.449 


1272.4 




152.367 


1847.5 


H 


178.285 


2529.4 


% 


126.842 


1280.3 


% 


152.760 


1857.0 


% 


178.678 


2540.6 


14 


127.2:35 


1288.2 


1 


153.153 


1866.5 


57. 


179.071 


2551.8 


% 


127.627 


1296.2 


153.545 


1876.1 


1 


179.463 


2563.0 


H 


128.020 


1304.2 


49. 


153.938 


1885.7 


179.856 


2574.2 


% 


128.413 


1312.2 


% 


154.331 


1895.4 


180.249 


2585.4 


41. 


128.805 


1320.3 


8 


154.723 


1905 




180.642 


2596.7 


% 


129.198 


1328.3 


155.116 


1914.7 


%k 


181.034 


2608.0 


8 


129.591 


1336.4 


P 


155.509 


1924.4 


% 


181.427 


2619.4 


129.983 


1344.5 


155.902 


1934.2 


181.820 


2630.7 


H 


130.376 


1352.7 




156.294 


1943.9 


58. 


182.212 


2642.1 


% 


130.769 


1360.8 


% 


156 687 


1953.7 


1 


182.605 


2653.5 


% 


131.161 


1369.0 


50. 


157.080 


1963.5 


182.998 


2664.9 


% 


131.554 


1377.2 


% 


157.472 


1973.3 




183.390 


2676.4 


42. 


131.947 


1385.4 


1 


157.865 


1983.2 


14 


183.783 


2687.8 


I 


132.340 


1393.7 


158.258 


1993.1 


% 


184.176 


2699.3 


132.732 


1402.0 




158.650 


2003.0 


S 


184.569 


2710.9 


133.125 


1410.3 


5/| 


159.043 


2012.9 


184.961 


2722.4 




133.518 


1418.6 


% 


159.436 


2022.8 


59. 


185.354 


2734.0 


% 


133.910 


1427.0 


% 


159.829 


2032.8 


1 


185.747 


2745.6 


9£ 


134.303 


1435.4 


51 


160.221 


2042.8 


186.139 


2757.2 


% 


134.696 


1443.8 


14 


160.614 


2052.8 


186.532 


2768.8 


43 


135.088 


1452.2 


« 


161.007 


2062.9 




186.925 


2780.5 


H 


135.481 


1460.7 


161.399 


2073.0 


% 


187.317 


2792.2 


% 


135.874 


1469.1 




161.792 


2083.1 


8 


187.710 


2803.9 


% 


136.267 


1477.6 


tS 


162.185 


2093.2 


188.103 


2815.7 


14 


136.659 


1486.2 


g 


162.577 


2103.3 


60 


188.496 


2827.4 


% 


137.052 


1494.7 


162.970 


2113.5 


% 


188.888 


2839.2 


¥a 


137.445 


1503.3 


53 


163.363 


2123.7 


8 


189.281 


2851.0 


% 


137.837 


1511.9 


8 


163.756 


2133.9 


189.674 


2862.9 


44 


138.230 


1520.5 


164.148 


2144.2 




190.066 


2874.8 


n 


138.023 


1529.2 


% 


164.541 


2154.5 


76 


190.459 


2886.6 


139.015 


1537.9 


14 


164.934 


2164.8 


M 


190.852 


2898.6 




139.408 


1546.6 


% 


165.326 


2175.1 


% 


191.244 


2910.5 


i2 


139.801 


1555.3 


1 


165.719 


2185.4 


61 


191.637 


2922.5 


% 


140.194 


1564.0 


166.112 


2195.8 


H 


192.030 


2934.5 


% 


140.586 


1572.8 


53 


166.504 


2206.2 


Ya 


192.423 


2946.5 


% 


140.979 


1581.6 


% 


166.897 


2216.6 




192.815 


2958.5 


45 


141.372 


1590.4 


H 


167.290 


2227.0 


L£ 


193.208 


2970.6 


M 


141.764 


1599.3 


% 


167.683 


2237.5 


% 


193.601 


2982.7 




142.157 


1608.2 


\i 


168.075 


2248.0 


1 


193.993 


2994.8 


% 


142.550 


•1617.0 


% 


168.468 


2258.5 


194.386 


3006.9 


1£ 


142.942 


1626.0 


% 


168.861 


2269.1 


62. 


194.779 


3019.1 


7& 


143. 3&5 


1634.9 


169.253 


2279.6 


% 


195.171 


3031.3 


s 


143.728 


1643.9 


54- 


169.646 


2290.2 


H 


195.564 


3043.5 


144.121 


1652.9 


M 


170. 039 


2300.8 




195.957 


3055.7 


46 


144.513 


1661.9 


S 


170.431 


2311.5 


1^ 


196.350 


3068.0 


^ 


144.906 


1670.9 


170.824 


2322.1 


vk 


196.742 


3080.3 


I 


145.299 


1680.0 


1 


171.217 


2332.8 


B 


197.135 


3092.6 




145.691 


1689.1 


171.609 


2343.5 


197.528 


3104.9 


*6 


146.084 


1698.2 


172.002 


2354.3 


63 


197.920 


3117.2 



194 



USEFUL TABLES. 



FIFTH ROOTS AND FIFTH POWERS, 

(Abridged from Trautwine.) 



° C 




® o 




® o 




oif 




k~ 




IS 


Power. 


6 q 


Power. 


6 o 


Power. 


o o 


Power. 


. o 
o o 


Power, 




£« 




£tf 




£« 




Itf 




.10 


.000010 


3.7 


693.440 


9.8 


90392 


21.8 


4923597 


40 


102400000 


.15 


.000075 


3.8 


792.352 


9.9 


95099 


22.0 


5153632 


41 


115856^:01 


.20 


.000320 


3.9 


902.242 


10.0 


100000 


22.2 


5392186 


42 


130691232 


.25 


.000977 


4.0 


1024.00 


10 2 


110408 


22.4 


5639493 


43 


147008443 


.30 


.002430 


4.1 


1158.56 


10.4 


121665 


22.6 


5895793 


44 


164916224 


.35 


.005252 


4.2 


1306.91 


10.6 


133823 


22.8 


6161327 


45 


184528)25 


.40 


.010240 


4.3 


1470.08 


10.8 


146933 


23.0 


6436343 


46 


205962976 


.45 


.018453 


4.4 


1649.16 


11.0 


161051 


23.2 


6721093 


47 


229345007 


.50 


.031250 


4.5 


1845.28 


11.2 


176234 


23.4 


7015834 


48 


254803968 


.55 


.050328 


4.6 


2059.63 


11.4 


192541 


23.6 


7320825 


49 


282475249 


.60 


.077760 


4.7 


2293.45 


11.6 


210C34 


23.8 


7636332 


50 


312500000 


.65 


.116029 


4.8 


2548.04 


11.8 


228776 


24.0 


7962624 


51 


345025251 


.70 


.168070 


4.9 


2824.75 


12.0 


248832 


24.2 


8299976 


52 


380204032 


.75 


.237305 


5.0 


3125.00 


12.2 


270271 


24.4 


8648666 


53 


418195493 


.80 


.327680 


5.1 


3450.25 


12.4 


293163 


24.6. 


9008978 


54 


459165024 


.85 


.443705 


5.2 


3802.04 


12.6 


317580 


24.8 


9381200 


55 


503284375 


.90 


.590490 


5.3 


4181.95 


12.8 


343597 


25.0 


9765625 


56 


550731776 


.95 


.773781 


5.4 


4591.65 


13.0 


371293 


25.2 


10162550 


57 


601692057 


1.00 


1.00000 


5.5 


5032.84 


13.2 


400746 


25.4 


10572278 


58 


656356768 


1.05 


1.27628 


5.6 


5507.32 


13.4 


432040 


25.6 


10995116 


59 


714924299 


1.10 


1.61051 


5.7 


6016.92 


13 6 


465259 


25.8 


11431377 


60 


777600000 


1.15 


2.01135 


5.8 


6563.57 


13.8 


500490 


26.0 


11881376 


61 


844596301 


1.20 


2.48832 


5.9 


7149.24 


14.0 


537824 


26.2 


12345437 


62 


916132832 


1.25 


3.05176 


6.0 


7776.00 


14.2 


577353 


26.4 


12823886 


63 


992436543 


1.30 


3.71293 


6.1 


8445.96 


14.4 


619174 


26.6 


13317055 


64 


1073741824 


1.35 


4.48403 


6.2 


9161.33 


14 6 


663383 


26.8 


13825281 


65 


1160290625 


1.40 


5.37824 


6.3 


9924.37 


14.8 


710082 


27.0 


14348907 


66 


1252332576 


1.45 


6.40973 


6.4 


10737 


15.0 


759375 


27.2 


14888280 


67 


1350125107 


1.50 


7.59375 


6.5 


11603 


15.2 


811368 


27.4 


15443752 


68 


1453933568 


1.55 


8.94661 


6.6 


12523 


15.4 


866171 


27»6 


16015681 


69 


1564031349 


1.60 


10.4858 


6.7 


13501 


15.6 


923896 


27.8 


16604430 


70 


1680700000 


1.65 


12.2298 


6.8 


14539 


15.8 


984658 


28.0 


17210368 


71 


1804229351 


1.70 


14.1986 


6.9 


15640 


16.0 


1048576 


28.2 


17833868 


72 


1934917632 


1.75 


16.3141 


7.0 


16807 


16.2 


1115771 


28.4 


18475309 


73 


2073071593 


1.80 


18.8957 


7.1 


18042 


16.4 


1186367 


28.6 


19135075 


74 


2219006624 


1.85 


21.6700 


7.2 


19349 


16.6 


1260493 


28.8 


19813557 


75 


2373046875 


1.90 


24.7610 


7.3 


20731 


16.8 


1338278 


29.0 


20511149 


76 


2535525376 


1.95 


28.1951 


7.4 


22190 


17.0 


1419857 


29.2 


21228253 


77 


2706784157 


2.00 


32.0000 


7.5 


23730 


17.2 


1505366 


29.4 


21965275 


78 


2887174368 


2.05 


36.2051 


7.6 


25355 


17.4 


1594947 


29.6 


22722628 


79 


3077056399 


2.10 


40 8410 


7.7 


27068 


17.6 


1688742 


29.8 


23500728 


80 


3276800000 


2.15 


45.9101 


7.8 


28872 


17.8 


1786899 


30.0 


24300000 


81 


3486784401 


2 20 


51.5363 


7.9 


30771 


18.0 


1889568 


30.5 


26393634 


82 


3707398432 


2.25 


57.6650 


8.0 


32768 


18.2 


1996903 


31.0 


28629151 


83 


3939040643 


2.30 


64.3634 


8.1 


34868 


18.4 


2109061 


31.5 


31013642 


84 


4182119424 


2.35 


71.6703 


8.2 


37074 


18.6 


2226203 


32.0 


33554432 


85 


4437053125 


2.40 


79.6262 


8.3 


39390 


18.8 


2348493 


32.5 


36259082 


86 


4704270176 


2.45 


88.2735 


8.4 


41821 


19.0 


2476099 


33.0 


39135393 


87 


4984209207 


2.50 


97.6562 


8.5 


44371 


19.2 


2609193 


33.5 


42191410 


88 


5277319168 


2.55 


107.820 


8.6 


47043 


19.4 


2747949 


34.0 


45435424 


89 


5584059449 


2.60 


118.814 


8.7 


49842 


19.6 


2892547 


34.5 


48875980 


90 


5904900000 


2.70 


143.489 


8.8 


52773 


19.8 


3043168 


35.0 


52521875 


91 


6240321451 


2.80 


172.104 


8.9 


55841 


20.0 


3200000 


35.5 


56382167 


92 


6590815232 


2.90 


205.111 


9.0 


59049 


20.2 


3363232 


36.0 


60466176 


93 


6956883693 


3.Q0 


243 000 


9.1 


62403 


20.4 


3533059 


36.5 


64783487 


94 


7339040224 


3.10 


286.292 


9.2 


65908 


20.6 


3709677 


37.0 


69343957 


95 


7737809375 


3.20 


335.544 


9.3 


69569 


20.8 


3893289 


37.5 


74157715 


96 


8153726976 


3.30 


391.354 


9.4 


73390 


21.0 


4084101 


38.0 


79235168 


97 


8587340257 


3.40 


454.354 


9.5 


77378 


21.2 


4282322 


38.5 


84587005 


98 


9039207968 


8.50 


525.. 219 


9.6 


81537 


21.4 


4488166 


39.0 


90224199 


99 


9509900499 


3.60 


604.662 


9.7 


85873 


21.6 


4701850 


39.5 


9615801.2 







USEFUL TABLES. 



195 





SQTJABES, CUBES AND RECIPROCALS. 


Hos. 


Squares. 


Cubes. 


Reciprocals. 


Nos. 


Squares. 


Cubes. 


Reciprocals. 


1 


1 


1 


1. 000000000 


51 


26 01 


132 651 


.019607843 


2 


4 


8 


.500000000 


52 


27 04 


140 608 


.0192:0769 


3 


9 


27 


.333333333 


53 


28 09 


148 877 


.018867925 


4 


16 


64 


.250000000 


64 


29 16 


157 464 


.018518519 


5 


25 


125 


.200000000 


55 


30 25 


166 375 


.018181818 


6 


36 


216 


.166666667 


56 


3136 


175 6f 6 


.017857143 


7 


49 


343 


.142857143 


57 


32 49 


185 193 


.017543860 


8 


64 


512 


.125000000 


58 


33 64 


195 112 


.017241379 


9 


81 


729 


.111111111 


59 


34 81 


205 379 


.016949153 


10 


100 


1000 


.100000000 


60 


36 00 


216 000 


.016666667 


11 


121 


1331 


.090909091 


61 


37 21 


226 981 


.016393443 


12 


144 


1728 


.083333333 


62 


38 44 


238 328 


.016129032 


13 


169 


2197 


.0T6923077 


63 


39 69 


250 047 


.015873016 


14 


196 


2 744 


.071428571 


64 


40 96 


262 144 


.015625000 


15 


225 


3 375 


.066666667 


65 


42 25 


274 625 


.015384615 


16 


2 56 


4 096 


.062500000 


66 


43 56 


287 496 


.015151515 


17 


2 89 


4 913 


.0588-23529 


67 


44 89 


3'.0 763 


.014925373 


18 


324 


5 832 


.055555556 


68 


46 24 


314 432 


.014705882 


19 


361 


6 859 


.052631579 


69 


47 61 


328 509 


.014492754 


20 


400 


8 000 


.050000000 


70 


49 00 


343 000 


.014285714 


21 


4 41 


9 261 


.047619048 


71 


50 41 


357 911 


.014081507 


22 


4 84 


10 618 


.045451545 


72 


5184 


373 2)8 


.013888889 


23 


5 29 


12 167 


.043478^60 


73 


53 29 


389 017 


.013698630 


24 


5 76 


13 824 


.041666667 


74 


54 76 


405 224 


.01:3513514 


25 


625 


15 625 


.0400000UO 


75 


56 25 


421 875 


.013333333 


26 


6 76 


17576 


.038461538 


76 


57 78 


438 976 


.013157895 


27 


729 


19 683 


.037037037 


77 


59 29 


456 5 !3 


.012987013 


28 


7 84 


21 952 


.035714286 


78 


60 84 


474 552 


.012820513 


29 


8 41 


24 389 


.034482759 


79 


62 41 


493 039 


.012658228 


SO 


9 00 


27 000 


.033333333 


80 


64 00 


512 000 


.012500000 


31 


9 61 


29 791 


.032258065 


81 


65 61 


531441 


.012345679 


32 


10 24 


32 768 


.031250000 


82 


67 24 


551 368 


.012195122 


33 


10 89 


35 937 


.03)303030 


83 


68J-9 


571 787 


.012048193 


34 


1156 


39 304 


.029411765 


84 


70 56 


592 704 


.011904762 


85 


12 25 


42 875 


.028571429 


85 


72 25 


614125 


.011764706 


36 


12 96 


46 656 


.027777778 


86 


73 96 


636 056 


.011627907 


37 


13 69 


50 653 


.027027027 


87 


75 69 


658 503 


.011494253 


38 


14 44 


51 872 


.026315789 


88 


77 44 


681472 


.011363636 


39 


15 21 


59 319 


.025641026 


89 


79 21 


704 969 


.011235955 


40 


16 00 


64 000 


.025000000 


90 


8100 


729 000 


.011111111 


41 


16 81 


68 921 


.024390244 


91 


82 81 


753 571 


.010989011 


42 


17 64 


74(188 


.023809524 


92 


84 64 


778 688 


.010869565 


43 


18 49 


79 507 


.023255814 


93 


86 49 


804 357 


.010752(>88 


44 


19 86 


85184 


.022727273 


94 


88 36 


830584 


.010638298 


45 


20 25 


91125 


.02.4222222 


95 


90 25 


857 375 


.010526316 


46 


2116 


97 336 


.091739130 


96 


9216 


884 736 


.010416667 


47 


22 09 


103 8*3 


.021276600 


97 


94 09 


912 673 


.010309278 


48 


23 04 


110 592 


.020K33333 


98 


96 04 


941192 


.OK); 04082 


49 


24 01 


117 649 


.020408163 


99 


98 01 


970299 


.010101010 


50 


25 CO 


125000 


.020000000 


100 


10000 


1000000 


.010000000 



196 



USEFUL TABLES. 



SQUARES, CUBES AND RECIPROCALS— Continued. 



Hos. 


Squares. 


Cubes. 


Reciprocals. 


Nos. 


Squares. 


Cubes. 


Reciprocals. 


101 


102 01 


1030 301 


.009900990 


151 


2 28 01 


3 442 951 


.006622517 


102 


104 04 


1 061 208 


.009803922 


152 


2 3104 


3 511808 


.006578947 


103 


106 09 


1 092 727 


.009708738 


153 


2 34 09 


3 581 577 


.006535948 


104 


108 16 


1 124 864 


.009615385 


154 


2 37 16 


3 652 264 


.006493.506 


105 


110 25 


1 157 62} 


,009523810 


155 


240 25 


3 723 875 


.006151613 


106 


112 36 


1 191 016 


.009433962 


156 


243 36 


3 796 416 


.006410256 


107 


114 49 


1 225 043 


.009345794 


157 


2 46 49 


3 869 893 


.006369427 


106 


116 64 


1 25^ 712 


.009259259 


158 


2 49 64 


3 944312 


.006329114 


109 


118 81 


1 295 029 


.009174312 


159 


2 52 81 


4 019 679 


.006289308 


110 


12100 


1331000 


.009090909 


160 


256 00 


4 096 000 


.006250000 


111 


1^23 21 


1 367 631 


.009009009 


161 


2 59 21 


4173281 


.006211180 


112 


125 44 


1 404 928 


.008928571 


162 


2 62 44 


4 2515 8 


.006172840 


113 


127 69 


1 442 897 


.008849558 


163 


2 65 69 


4 330 747 


.006134969 


114 


129 96 


1 481 544 


.008771930 


164 


2 68 96 


4 410 944 


.00609-561 


115 


132 25 


1 520 875 


.008695652 


165 


2 72 25 


4 492125 


.006060608 


116 


1 34 56 


1 560 896 


.008620690 


166 


2 75 56 


4 574 296 


.006021096 


117 


136 89 


1601 6 L3 


.008547009 


167 


2 78K9 


4 657 463 


.005988024 


118 


139 24 


16*3 032 


.008474576 


168 


2 82 24 


4 741 632 


.005952381 


119 


14161 


1 685 159 


.008403361 


169 


2 85 61 


4 826 809 


.005917160 


120 


144 00 


1728 000 


.008333333 


170 


2 89 00 


4 913 000 


.005882353 


121 


146 41 


1 771 561 


.008264463 


171 


2 92 41 


5000211 


.005847953 


122 


148 84 


1 815 848 


.008196721 


172 


2 95 84 


5 088 448 


.005813953 


123 


15129 


1 860 867 


.008130081 


173 


2 99 29 


5 177 717 


.005780347 


124 


153 76 


1 906 624 


.008064516 


174 


3 02 76 


5 268 024 


.005747126 


125 


156 25 


1 953 125 


.008000000 


175 


3 06 25 


5 359 375 


.005714286 


126 


1 58 76 


2 000 376 


.007936508 


176 


3 09 76 


5 451 776 


.005681818 


127 


16129 


2 048 3S3 


.007874016 


177 


3 13 29 


5 545 233 


,0i 156(9718 


128 


163 84 


2 097 152 


.007812500 


178 


3 16 84 


5 659 752 


.005617978 


129 


166 41 


2 146 6S9 


.007751938 


179 


3 20 41 


5 735 339 


.005566592 


130 


169 00 


2 197 000 


.017692308 


180 


.3 24 00 


5 832 000 


.005555556 


131 


17161 


2 248 091 


.007633588 


181 


3 27 61 


5 929741 


.005524862 


132 


1 74 24 


2 293 968 


.007575758 


182 


3 3124 


6 028 568 


.005494505 


133 


176 89 


2 352 637 


.007-il8797 


183 


3 34 89 


6 128 487 


.005464481 


J 34 


179 56 


2 406 104 


.007462687 


184 


3 38 56 


6 229 504 


.005434783 


135 


182 25 


2 460 375 


,007407407 


185 


3 42 25 


6 331 625 


.005405405 


136 


184 96 


2 515 456 


.007352941 


186 


3 45 96 


6 434 856 


.005376344 


137 


187 69 


2 571 353 


.007299270 


187 


3 49 69 


6 539 203 


.005347594 


138 


190 44 


2 628 072 


,007246377 


188 


35341 


6 644 672 


.005319149 


139 


193 21 


2 685 619 


.007 194 '45 


189 


3 57 21 


6 751 239 


. 00529 H '05 


140 


196 00 


2 744 000 


.007142857 


190 


3 6100 


6 859 000 


.005263158 


141 


198 81 


2 803 221 


.007092199 


191 


3 64 81 


6 967 871 


.005235602 


142 


2 0164 


2 863 288 


.007042254 


192 


3 68*4 


7 077 888 


.005208333 


113 


2 04 49 


2 924 207 


.006993007 


193 


3 72 49 


7189 057 


.005181347 


144 


2 07 36 


2 985 984 


.006914144 


194 


3 76 36 


7 301 384 


.005154639 


145 


210 25 


3 048 625 


.006898552 


195 


380 25 


7 414 875 


,005128205 


146 


21316 


6 112 136 


.006819315 


196 


3 84 16 


7 529 536 


.005102041 


147 


2 16 09 


3 176 523 


.006802721 


197 


388 09 


7 645 373 


.005076142 


148 


21904 


3 241 792 


.006756757 


108 


3 92 01 


7 762 392 


.005050505 


149 


2 22 01 


3 307 949 


.006711409 


199 


3 96 01 


7 880 599 
60OOOOO 


.005025126 


150 


225 00 


3 375 000 


• .006666667 


200 


400 00 


.005000000 



USEFUL TABIDS. 



I 9 7 



SQUARES, CUBES AND RECIPROCALS— Continued. 



Hos, 


Squares. 


Cubes. 


Reciprocals. 


Kos. 


Squares. 


Cubes. 


Reciprocals. 


201 


4 04 01 


8 120 601 


.004975124 


251 


6 30 01 


15 813 251 


.003934061 


202 


4 08 04 


8 242 408 


.004950495 


252 


635 04 


16 003 008 


.003968254 


203 


4 12 09 


8 365 427 


.034926108 


253 


6 40 09 


16 194 277 


.003952569 


204 


4 16 16 


8 489 661 


.004901961 


254 


6 45 16 


16 387 064 


.003937008 


205 


4 20 25 


8 615 125 


.004878049 


255 


6 50 25 


16 581375 


.003921569 


206 


• 4 24 36 


8 741 816 


.004854369 


256 


6 55 36 


16 777 216 


.003906250 


207 


4 28 49 


8 869 743 


.004830918 


257 


6 60 49 


16 974 593 


.003891051 


208 


4 32 64 


8 998 912 


.004807692 


258 


6 65 64 


17173 512 


.003875969 


209 


4 36 81 


9 129 329 


.004784689 


259 


6 70 81 


17 373 979 


.003861004 


210 


4 4100 


9 261 000 


.001761905 


260 


6 76 00 


17 576 000 


.003846154 


211 


4 45 21 


9 393 931 


.004739336 


261 


6 8121 


17 779 581 


.003831418 


212 


4 49 44 


9 528 128 


.0J4716981 


262 


6 86 44 


17 984 728 


.003816794 


213 


4 53 69 


9 663 597 


.004694836 


263 


6 9169 


18 191 447 


.003802281 


214 


4 57 96 


9 800 344 


.004672897 


264 


6 96 96 


18 399 744 


.003787879 


215 


4 62 25 


9 938 375 


.004651163 


265 


7 02 25 


18 609 625 


.003773585 


216 


4 66 56 


10 077 696 


.004629630 


266 


7 07 56 


18 821 096 


.003759398 


217 


4 70 89 


10 218 313 


.004608295 


267 


7 12 89 


19 034 163 


.003745318 


218 


4 75 24 


10 360 232 


.0045*7156 


268 


718 24 


19 248 832 


.003731343 


2! 9 


4 79 61 


10 503 459 


.004566210 


269 


7 23 61 


19 465 109 


.003717472 


220 


4 84 00 


10 648 000 


.004545155 


270 


7 29 00 


19 683 000 


.003703704 


221 


4 88 41 


10 793 861 


.004524887 


271 


7 34 41 


19 902 511 .003690037 


222 


4 92 84 


10 941 048 


.004504505 


272 


7 39 84 


20 123 648 


.003676471 


223 


4 97 29 


11089567 


.004484305 


273 


7 45 29 


20 346 417 


.003663004 


224* 


5 0176 


11239 424 


.004464286 


274 


7 50 76 


20 570 824 


.003649635 


225 


506 25 


11 390 625 


-.004444444 


275 


7 56 25 


20 796 875 


.003366364 


226 


510 76 


11 543 176 


.004424779 


276 


7 6176 


21 024 576 


.003623188 


227 


515 29 


11697 083 


.001405286 


277 


7 67 29 


21 253 933 


.003610108 


228 


519 84 


11 852 352 


.004-385965 


278 


7 72 84 


21 484 952 


.003597122 


229 


52441 


12 0)8 989 


.004366812 


279 


7 78 41 


21 717 639 


.003584229 


230 


5 29 01) 


12167 000 


.001347826 


280 


7 84 00 


21 952 000 


003571429 


231 


6 33 61 


12 326 391 


.004329004 


281 


7 89 61 


. 22 188 041 


.U03558719 


232 


5?8 24 


12 487 163 


.004310:345 


232 


7 95 24 


22 425 768 


.003546099 


233 


5 42 89 


12 649 337 


.0)4291845 


283 


8 00 89 


22 665 187 


.003533569 


234 


5 47 56 


12 812 904 


.00427.3504 


284 


806 56 


22 906 304 


.003521127 


235 


.5 52 25 


12 977 875 


.004255319 


285 


812 25 


23 149 125 


.003508772 


236 


5 56 96 


13 144 256 


.004237288 


286 


817 96 


23 393 656 


.003496503 


237 


5 6169 


13 312 053 


.004219409 


287 


8 23 69 


23 639 903 


.003484321 


238 


5 66 44 


13 481 272 


.004-01681 


288 


829 44 


23 887 872 


.003472222 


239 


5 7121 


13 651919 


.004184100 


289 


8 35 21 


24 137 569 


.003460208 


240 


5 76 00 


13 824 000 


.004166667 


290 


8 4100 


24 389 000 


.003448276 


241 


5 80 81 


13 997521 


.004149378 


291 


8 46 81 


24 642 171 


.003436426 


242 


5 85 64 


14172 488 


.004132231 


292 


8 52 64 


24 897 088 


.003424658 


243 


5 90 49 


14 348 907 


.004115226 


293 


8 58 49 


25 153 757 


.003412969 


244 


5 95 86 


14 526 784 


.004098361 


294 


8 64 36 


25 412 184 


,003401861 


245 


6 00 25 


14 706 125 


.004081633 


295 


8 70 25 


25672 375 


.003389831 


246 


6 05 16 


14 886 936 


.004065041 


296 


8 7616 


25 934 336 


.003378378 


247 


6 10 09 


15 069 223 


.004048583 


297 


8 82 09 


26 19S 073 


.003367003 


218 


615 04 


15 252 992 


.004032258 


298 


8 88 04 


26463 592 


.003355705 


249 


6 20 01 


15 438 249 


.004019064 


299 


8 94 01 


26 730 899 


.003344482 


250 


6 25 00 


15 625 000 


.004000000 


300 


900 00 


27 000 000 


.003333333 



198 



USKFUIv TABLES. 



SQUARES, CUBES AND RECIPROCALS— Continued. 



flos. 


Squares Cubes. 


Reciprocals. J Nos. 


Squares. 


Cubes. 


Reciprocals. 


801 


9 06 01 


27 270 901 


.003322259 1 351 


12 32 01 


43 243 551 


.002849003 


802 


912 04 


27 543 608 


.003311258 


352 


12 39 04 


43 614 208 


.002840909 


803 


918 09 


27 818 127 


.003300330 


353 


12 46 09 


43 986 977 


.002832861 


304 


92416 


28 094 464 


.003289474 


354 


12 53 16 


44 361864 


.002824859 


305 


93025 


28372 625 


.008278689 


355 


126025 


44 738 875 


.002816901 


306 


03*36 


28652616 


.003267974 


356 


12 6736 


45118016 


.002808989 


307 


9 42 49 


28934443 


.003257329 


357 


12 74 49 


45 499 293 


.002801120 


303 


9 48 64 


29 218 112 


.003246753 


358 


12 8164 


45 882 712 


.002793296 


309 


9 54 81 


29 503 629 


.003236246 


359 


12 88 81 


46 268 279 


.002785515 


310 


Q6100 


29 791000 


.003225806 


860 


12 96 00 


46 656000 


.002777778 


311 


96721 


30080231 


.003215434 


361 


1303 21 


47 045 881 


.002770083 


312 


97344 


30 371 328 


.003205128 


362 


13 10 44 


47 437 928 


.002762431 


313 


9 79 69 


30 664 297 


.0-3194888 


363 


13 17 69 


47 832 147 


.002754821 


314 


9 85 96 


30 959 144 


.003184713 


364 


13 24 96 


48 228 544 


.002747253 


315 


9 9225 


31255 875 


.003174603 


365 


13 3225 


48 627125 


.002739726 


316 


9 98 56 


31554 496 


.003164557 


366 


133956 


49 027896 


.002782240 


317 


10 04 89 


31 855 013 


.003154574 


367 


13 46 89 


49 430 863 


.002724796 


318 


101124 


32 157 432 


.003144654 


368 


13 54 24 


49 836 032 


.002717891 


319 


101761 


32461759 


.003134796 


369 


13 61 61 


50 243 409 


.002710027 


320 


1024 00 


32 768000 


.003125000 


370 


13 69 00 


60 653 000 


.002702703 


821 


10 3041 


83 076 161 


.003115265 


371 


13 76 41 


61064 811 


.002695418 




1036 84 


33 386 248 


.003105590 


372 


13 83 84 


61 478 848 


,002688172 


323 


10 43 29 


33 698 267 


.003095975 


373 


13 9129 


51 895 117 


.002680965 


324 


10 49 76 


34 012 224 


.003086420 


374 


13 98 76 


62 313 624 


.002673797 


325 


1056 25 


34 328125 


.003076923 


375. 


1406 25 


62 734375 


.002666667 


326 


106276 


34 645976 


.003067485 


376 


1413 76 


53 157 376 


.002659574 


327 


10 69 29 


34 965 783 


.003058104 


377 


14 2129 


53 582 633 


.002652520 




10 75 84 


35 287 552 


.003048780 


378 


14 28 84 


54 010 152 


.002645503 


329 


10 82 41 


35 611 289 


.003039514 


379 


14 36 41 


54 439 939 


.002638522 


330 


10 89 00 


35 937000 


.003030303 


380 


14 44 00 


64 872 000 


.002631679 


331 


1095 61 


36 264 691 


.003021148 


381 


14 51 61 


65 306 341 


.002624672 


332 


1102 24 


36 594 368 


.003012048 


382 


14 59 24 


55 742 968 


.002617801 




11 08 89 


36 926 037 


.003003003 


383 


14 66 89 


66 181 887 


.002610966 


m 


1115 56 


37 259 704 


.002994012 


384 


14 74 56 


56 623 104 


.002604167 


335 


112225 


37 595 375 


.002985075 


385 


14 82 25 


67066 625 


.002597403 


336 


1128 96 


37 933056 


.002976190 


386 


14 89 96 


67 512 456 


.002590674 


237 


1135 69 


38 272 753 


.002967359 


387 


14 97 69 


67 960 603 


.002583979 


83S 


1142 44 


38 614 472 


.002958580 


388 


15 05 44 


58 411 072 


.002-577320 


.'(39 


1149 21 


38 958 219 


.002949853 


389 


15 13 21 


68 863 869 


.002570694 


3-10 


1156 00 


39 304 000 


.002941176 


390 


15 2100 


69 319 000 


.002564103 


341 


11 62 81 


39 651 821 


.002932551 


391 


15 28 81 


59 776 471 


.002557645 




11 69 64 


40 001 688 


.002923977 


392 


15 36 64 


60 236 288 


.002551020 


343 


1176 49 


40 353 607 


.0029 5452 


303 


15 44 49 


60 698 457 


.002544529 


344 


11 83 36 


40 707 584 


.002906977 


394 


15 52 36 


61162 984 


.002538071 


345 


1199 25 


41063 625 


.002898551 


395 


1560 25 


61629 875 


.002531646 


3<6 


1197 16 


41 421 736 


.002890173 


396 


15 6816 


62 099 136 


.002525253 


347 


12 04 09 


41 781923 


,002881844 


397 


15 76 09 


62 570 773 


.002518892 


348 


121104 


42144192 


,0028' 7 356i 


398 


15 84 04 


63 044 792 


.002512563 


340 


12 18 01 


42 508 549 


.002865330 


309 


15 92 01 


63 521 199 


.002.506265 


350 


12 25 00 


42 875 000 


.002857143 


400 


16 00 00 


64 000 000 


.002500000 



USEFUL TABIDS. 



199 



SQUARES, CUBES AND RECIPROCALS— Continued. 



Nos. 


Squares. 


Cubes. 


Reciprocals. 


flos. 


Squares. 


Cubes. 


Reciprocals. 


401 
402 
403 
404 
405 


16 03 01 
16 16 04 
16 24 09 
16 32 18 
1640 25 


61 481 201 

64 964 808 

65 450 827 

65 939 264 

66 430 125 


.002493766 
.002487562 
.002481390 
.002475248 
.002469136 


451 
452 
453 
454 
455 


20 3101 
20 43 04 

20 52 09 
20 6116 
20 70 25 


91 733 851 

92 345 408 

92 959 677 

93 576 664 

94 196 375 


.002217295 
.002212389 
.002207506 
.002202643 
.002197802 


406 
407 
408 
409 
410 


1648 36 
16 56 49 
16 64 64 
1672 81 
168100 


66 923 416 

67 419 143 

67 917 312 

68 417 929 
68 921000 


.002463054 
.002457002 
.002450980 
.002444988 
.002439024 


456 
457 
458 
459 
460 


20 79 36 
20 88 49 

20 97 64 

21 06 81 
21 16 00 


94 818 816 

95 443 993 

96 071 912 

96 702 579 

97 336 000 


.002192982 
.002188184 
.002183406 
.002178649 
.002173913 


411 

412 
413 
414 
415 


16 89 21 

16 97 44 

17 05 69 
17 13 96 
17 22 25 


69426 531 

69 931 528 
70444 997 

70 957 944 
71473 375 


.002433090 
.002427184 
.002421308 
.002415459 
.002489639 


461 
462 
463 
464 
465 


2125 21 
2134 44 
21 43 69 
21 52 96 
2162 25 


97 972181 

98 611 128 

99 252 847 
99 897 344 

100544 625 


.002169197 
.002164502 
.002159827 
.002155172 
.002150538 


41G 
417 
418 
419 

420 


17 30 56 
17 38 89 
17 47 24 
17 55 61 
17 64 00 


71 991 296 

72 51! 713 

73 034 632 
73560 059 
74088 000 


.002403846 
.002398082 
.002392344 
.002386635 
.002380952 


466 
467 
468 
469 
470 


217156 
218089 
21 90 24 

21 99 61 

22 0900 


101 194 696 
101847563 

102 503 232 

103 161 709 
103 823000 


.002145928 
.U02141328 
.002136752 
.002132196 
.002127660 


421 
422 
423 
424 
425 


17 72 41 
17 8084 
17 89 29 

17 97 76 

18 0625 


74 618 461 

75 151 448 

75 686 967 

76 225 024 
76 765 625 


.002375297 
.002369668 
.002364066 
.002358491 
.002352941 


471 

472 
473 
474 

475 


2218 41 

22 27 84 
22 37 29 
22 46 76 
22 56 25 


104 487 111 
105154 048 

105 823 817 

106 496424 
107 171 875 


.002123142 
.002118644 
.002114165 
.002109705 
.002105263 


426 
427 
428 
429 
430 


1.8 14 76 

18 23 29 
18 3184 
18 40 41 
18 49 00 


77 308776 

77 854 483 

78 402 752 

78 953589 

79 507 000 


.002347418 
.002341920 
.002336449 
.002331002 
.002325581 


476 
477 
478 
479 
480 


22 6576 
22 75 29 
2284 84 
22 94 41 
230400 


107 850176 

108 531333 

109 215 352 
109902239 
110692 000 


.002100840 
.002096436 
.002092050 
.002087683 
.002083383 


431 
432 
43} 
434 
435 


18 57 61 
18 63 21 
18 74 89 
18 83 56 
18 92 25 


80 062 991 

80 621 568 
81 182 737 

81 746 504 

82 312 875 


.002320186 
.002314815 
.002309469 
.002304147 
.002298851 


481 

482 
483 

484 
485 


2313 61 
2328 24 
2332 89 
2342 56 
236225 


111281611 

111 980 168 

112 678587 

113 379 904 

114 084 125 


.002079002 
.002074689 
.002070393 
.002066116 
.002061856 


436 
437 
438 
439 
4)0 


19 00 96 
19 09 69 
19 18 44 
19 27 21 
19 36 00 


82 881856 
83453 453 
81027 672 
84 604 519 
85184 000 


.002293578 

.002288330 
.002283105 
.002277904 
.002272727 


486 
487 
488 
489 
490 


23 6196 
23 7169 
23 8144 

23 91 21 

24 0100 


114 791 256 

115 501 303 

116 214 272 

116 930169 

117 649 000 


.002057613 
.002053388 
.002049180 
.002044990 
.002040816 


441 
442 
443 
444 
445 


19 44 81 
19 53 61 
19 62 49 
19 71 36 
19 80 25 


85 766 121 

86 350 888 
86 938 307 
87528 384 
88121125 


.002267574 
.002262443 
.002257336 
.002252252 
.002247191 


491 
492 
493 
494 
495 


211081 
24 20 64 
24 30 49 
24 40 36 
215025 


118870771 

119 095 488 

119 823 157 

120 553 784 
121287375 


.002036660 
.0020*2520 
.002028398 
.002024291 
,002020202 


446 
447 
448 
449 

450 


19 8916 

19 98 09 

20 07 01 
20 16 01 
20 23 00 


88716 536 
89 314 623 

89 915 392 

90 518849 
91125 000 


.00224215Z 
.0;)2237136 
.002232143 
,0022271m 

.002222222 


496 
497 

498 
499 
500 


24 60 16 
24 70 09 
24 80 04 

24 90 01 

25 00 00 


122 023936 
122763 473 

123 505 992 

124 251 499 

125 000 000 


.002016129 

.002012072 
.002008032 
.002004008 
.002000000 



USEffUI, TABLES. 



TEIttPEKATUKES, CENTIGRADE AND 
FAHRENHEIT. 



c. 


F. 


c. 


F. 


C. 


F. 


C. 


F. 


C. 


F. 


C. 


F. 


C. 


F. 


-40 


-40. 


26 


78.8 


92 


197.6 


158 


316.4 


224 


485.2 


2&0 


554 


950 


1742 


-39 


-38.2 


27 


80.6 


93 


199.4 


159 


818. 2 


225 


437. 


.300 


572 


960 


1760 


-38 


-36.4 


28 


82.4 


94 


201.2 


160 


320. 


226 


438.8 


310 


590 


970 


1778 


-37 


—34 6 


29 


84.2 


95 


203. 


161 


821.8 


227 


440.6 


320 


608 


980 


1796 


-36 


—32.8 


30 


86. 


96 


204.8 


162 


323.6 


228 


442.4 


W 


626 


990 


1814 


-35 


-31. 


31 


87.8 


97 


206. a 


163 


825.4 


229 


444.2 


H r ~ 


644 


1000 


1832 


-34 


—29.2 


32 


89.6 


98 


208.4 


164 


327.2 


230 


446. 


f-.",0 


662 


1010 


1850 


-33 


—27.4 


33 


91.4 


99 


210.2 


165 


329. 


231 


447.8 


,-r 


680 


1020 


1868 


-32 


-25.6 


34 


93.2 


100 


212. 


166 


380.8 


232 


449.6 


370 


698 


1030 


1886 


-31 


-23.8 


35 


95. 


101 


213.8 


167 


332.6 


233 


451.4 


.380 


716 


1040 


1904 


-30 


-22. 


36 


96.8 


102 


215.6 


168 


334.4 


234 


453.2 


■:A 


734 


1050 


1922 


-29 


-20.2 


37 


98.6 


103 


217.4 


169 


336.2 


235 


455. 


400 


752 


1060 


1940 


-28 


-18.4 


33 


100.4 


104 


219.2 


170 


338. 


236 


456.8 


4!0 


770 


1070 


1958 


-27 


-16.6 


39 


102.2 


105 


221. 


171 


339.8 


237 


458.6 


420 


788 


1080 


1976 


-26 


-14.8 


40 


104. 


106 


222.8 


172 


341.6 


238 


460.4 


430 


806 


1090 


1994 


-25 


-13. 


41 


105.8 


107 


224. Q 


173 


343.4 


239 


462.2 


440 


824 


1100 


2012 


-24 


-11.2 


42 


107.6 


108 


226.4 


174 


345.2 


240 


464. 


450 


842 


1110 


2030 


-28 


- 9.4 


43 


109.4 


109 


228.2 


175 


347. 


241 


465.8 


460 


860 


1120 


2048 


-22 


-7.6 


44 


111.2 


110 


230. 


176 


348.8 


242 


487.6 


470 


878 


1130 


2066 


-21 


— 5.8 


45 


118. 


111 


231.8 


177 


350.6 


243 


469.4 


480 


896 


1140 


2084 


-20 


- 4. 


-,, 


114.8 


112 


233 6 


178 


352.4 


244 


471.2 


;.:-■•:< 


914 


1150 


2102 


-19 


- 2.2 


4? 


116.6 


113 


235.4 


179 


354.2 


245 


478. 


500 


932 


1160 


2120 


-18 


- 0.4 


48 


118.4 


114 


237.2 


180 


856. 


246 


474.8 


510 


950 


il70 


2138 


-17 


+ 1.4 


49 


120.2 


115 


239. 


181 


357.8 


247 


476.6 


55.0 


968 


1180 


2156 


-18 


3.2 


50 


122. 


116 


240.8 


182 


359.6 


248 


478.4 


ooC 


986 


1190 


2174 


-15 


5. 


51 


123.8 


117 


242.6 


183 


361.4 


249 


480.2 


"■:■-;: 


1004 


1200 


2192 


-14 


6.8 


5S 


125.6 


118 


244.4 


184 


363.2 


250 


482. 


: V. 


1022 


1210 


2210 


-13 


8.6 


53 


127.4 


119 


246.2 


185 


365. 


251 


483.8 


560 


1040 


1220 


2228 


-12 


10.4 


54 


129.2 


120 


248. 


186 


366.8 


252 


485.6 


c/( 


1058 


1230 


2246 


-11 


12.2 


55 


131. 


121 


249.8 


187 


368.6 


253 


487.4 


m. 


1076 


1240 


2264 


-10 


14. 


56 


132.8 


122 


251.8 


188 


370.4 


254 


489.2 


590 


1094 


1250 


2282 


- 9 


15.8 


57 


134.6 


123 


253.4 


189 


372.2 


255 


49r. 


600 


1112 


1260 


2300 


- 8 


17.6 


58 


136.4 


124 


255.2 


190 


374. 


256 


492.8 


'/,i 


1130 


1270 


2318 


- 7 


19.4 


59 


138.2 


126 


257. 


191 


375.8 


257 


494.6 


620 


1148 


1280 


2336 


- 6 


21.2 


60 


140. 


126 


258.8 


192 


377.6 


258 


496.4 


..: 


1166 


1290 


2354 


- 5 


23. 


61 


141.8 


127 


260.6 


193 


379.4 


259 


498,2 


- 


1184 


1300 


2372 


- 4 


24.8 


62 


143.6 


128 


262.4 


194 


381.2 


260 


500. 


650 


1202 


1310 


2390 


- 3 


26.6 


63 


145.4 


129 


264.2 


195 


383. 


261 


501.8 


660 


1220 


1320 


2408 


- 2 


28.4 


64 


147.2 


130 


266. 


196 


384.8 


262 


303.6 


670 


123# 


1330 


2426 


- 1 


80.2 


65 


149. 


131 


267.8 


197 


386.6 


263 


505.4 


1680 


1256 


1340 


2444 





32. 


66 


150.8 


132 


269.6 


198 


388.4 


264 


507.2 


6v30 


1274 


135C 


2462 


f 1 


33.8 


67 


152.6 


133 


271.4 


199 


890.2 


265 


509. 


\ 


1292 


1360 


2480 


2 


35.6 


68 


154.4 


134 


273.2 


200 


392. 


266 


510.8 


710 


1810 


1870 


2498 


8 


37.4 


69 


156.2 


135 


275. 


201 


393.8 


267 


512.6 


72011828 


138C 


2516 


4 


39.2 


70 


158. 


136 


276.8 


202 


395.6 


268 


514.4 


780 1346 


1390 


2534 


5 


41. 


71 


159.8 


137 


278.6 


203 


397.4 


269 


616.2 


74011364 


1400 


2552 


6 


42.8 


72 


161.6 


138 


280.4 


204 


399.2 


270 


518. 


750 


1382 


1410 


2570 


7 


44.6 


n 


163.4 


139 


282.2 


205 


401. 


271 


519.8 


76C 


1400 


1420 


2588 


8 


46.4 


74 


165.2 


140 


284. 


206 


402.8 


272 


521.6 


770 


1418 


1430 


2606 


9 


48.2 


75 


167. 


141 


285.8 


207 


404.6 


273 

274 


523.4 


78C 


1436 


1440 


2624 


10 


50. 


76 


168.8 


142 


287.6 


208 


406.4 


525.2 


7&0 


1454 


1450 


2642 


11 


5T.8 


77 


170.6 


143 


289.4 


209 


408.2 


225 


527. 


800 


1472 


1460 


2660 


12 


53.6 


78 


172.4 


144 


291.2 


210 


410. 


276 


528.8 


810 


1490 


1470 


2673 


13 


55.4 


79 


174.2 


145 


293. 


211 


411.8 


277 


530.6 


820 


1508 


1480 


269(r 


14 


57.2 


80 


176. 


146 


294.8 


212 


413.6 


278 


532.4 


830 


1526 


1490 


2714 


£ 


59. 


81 


177.8 


147 


296.6 


213 


415.4 


279 


534.2 


610 


1544 


1500 


2732 


16 


60.8 


'A 


179.6 


148 


298.4 


214 


417.2 


280 


536. 


,<-,- 


1562 


1510 


2750 


S 


62.6 


83 


181.4 


149 


300.2 


215. 


419. 


281 


537.8 


860 


1580 


1520 
1530 


2768 


64.4 


84 


183.2 


150 


302. 


216 


420.8 


282 


539.6 


870 


1598 


2786 


19 


66.2 


85 


185.- 


151 


303.8 


217 


422,6 


283 


541.4 


880 


1616 


1540 


2804 


20 


68. 


86 


186.8 


152 


305.6 


218 


424.4 


284 


543.2 


890 


1634 


1550 


2822 


J21 


69.8 


87 


188.6 


153 


307.4 


219 


426.2 


285 


545. 


900 


1652 


1600 


2912 


22 


71.6 


88 


190.4 


154 


309.2 


220 


428. 


286 


546.8 


910 


1670 


1650 


3002 


23 


73.4 


89 


192.2 


155 


311. 


221 


429.8 


287 


548.6 


920 


1688 


1700 


3092 


24 


75.2 


90 


194. 


156 


312.8 


222 


431.6 


288 


550.4 


930 


1706 


1750 


3182 


25 


77. 


91 


195.8 


157 


314.6 


223 


433.4 


289 


552.2 


940 


1724 


1800 


8272 



USEFUL TABLES. 





1 


E3 


IPER 


ATI 


LIRE 


S, FAHRENHEIT AND 








CENTIGRAUE. 


F. 


C. 


F. 
26 


C. 


F 

92 


C. 

33.3 


F 
158 


C. 

70. 


F. 
224 


c. 


F. 


C. 


F. 


C. 


-40 


-40. 


-3.3 


106.7 


290 


143.3 


360 


182.2 


—39 


-39.4 


27 


- 2.8 


93 


33.9 


159 


70.6 


225 


107.2 


291 


143.9 


370 


187.8 


-38 


-38.9 


28 


— 2 2 


94 


34.4 


100 


71.1 


226 


107.8 


202 


144.4 


380 


193.3 


-37 


-38.3 


29 


— 1.7 


95 


35. 


161 


71.7 


227 


108.3 


im 


145. 


890 


198.9 


-36 


-37.8 


30 


- 1.1 


96 


35.6 


162 


72.2 


228 


108.9 


294 


145.6 


400 


204.4 


-35 


-37.2 


31 


- 0.6 


97 


36.1 


163 


72.8 


229 


109.4 


295 


146.1 


410 


210. 


-34 


-36.7 


32 


0. 


98 


36.7 


164 


73.3 


230 


110. 


220 


146.7 


420 


215.6 


-33 


-36.1 


33 


-f 0.6 


99 


37.2 


165 


73.9 


23! 


110.6 


297 


147.2 


480 


221.1 


-32 


—35.6 


34 


1.1 


100 


37.8 


166 


74.4 


232 


111.1 


228 


147.8 


410 


226.7 


-31 


-35, 


35 


1.7 


101 


.38.3 


167 


75 




111.7 


299 


148.3 


4.50 


232 2 


-30 


—34.4 


36 


2.2 


102 


38.9 


168 


75.6 


234 


112.2 


300 


148.9 


460 


237.8 


—29 


-33.9 


87 


2.8 


103 


"39.4 


169 


76.1 




112.8 


301 


149 4 


470 


243.3 


—28 


-33.3 


38 


3.3 


104 


40. 


170 


76.7 


236 


113.3 


302 


150. 


480 


248 9 


-27 


-32.8 


39 


3.9 


105 


40.6 


171 


77.2 


237 


113.9 


825' 


150.6 


490 


254.4 


—26 


-32.2 


40 


4.4 


106 


41.1 


572 


77 8 


2-8 


114.4 


301 


151.1 


500 


260. 


—25 


-31.7 


41 


5. 


107 


41.7 


173 


78.3 


239 


115. 


305 


151.7 


510 


265.6 


—24 


-31.1 


42 


5.6 


108 


42.2 


174 


78.9 


24(. 


115.6 


220 


152.2 


520 


271.1 


-23 


-30.6 


43 


6.1 


109 


42.8 


175 


79.4 


211 


116.1 


So; 


152.8 


5.30 


276.7 


-22 


—30. 


44 


6.7 


110 


43.3 


176 


80. 


242 


116.7 


-,,8 


153.3 


540 


282.2 


-21 


—29.4 


45 


7.2 


111 


43.9 


177 


80.6 


243 


117.2 


309 


153.9 


550 


287.8 


-20 


-28.9 


46. 


7.8 


112 


44 4 


178 


81.1 


244 


117.8 


310 


154.4 


560 


293.3 


-19 


-28.3 


47 


8.3 


113 


45. 


179 


81.7 


245 


118.3 


311 


155. 


570 


298.9 


-18 


-27.8 


48 


8.9 


114 


45.6 


ISO 


82.2 


246 


118.9 


312 


155.6 


580 


304.4 


-17 


—27.2 


49 


9.4 


115 


46.1 


181 


82.8 


247 


119.4 


313 


156.1 


590 


310. 


-16 


—26.7 


50 


10. 


116 


46.7 


182 


83.3 


2J8 


120. 


314 


156.7 


600 


315.6 


-15 


-26.1 


51 


10.6 


117 


47.2 


183 


83.9 


249 


120.6 


315 


157.2 


61.0 


321.1 


-14 


-25.6 


52 


11.1 


118 


47.8 


lti4 


84.4 


s,<, 


121.1 


316 


157.8 


620 


326.7 


—13 


-25. 


53 


11.7 


119 


48.3 


185 


85. 


251 


121.7 


317 


158.3 


©so 


332.2 


-12 


—24.4 


54 


12.2 


120 


48.9 


186 


85.6 


2 re 


122.2 


ole 


158.9 


640 


337.8 


—11 


-23.9 


55 


12.8 


121 


49.4 


187 


86.1 


253 


122.8 


319 


159.4 


650 


343.3 


—10 


-23.3 


58 


13.3 


122 


50. 


is> 


86.7 


254 


123.3 


J 


160. 


660 


348.9 


- 9 


-22.8 


57 


13.9 


123 


50.6 


189 


87.2 


255 


123.9 


821 


160.6 


670 


354.4 


- 8 


—22.2 


58 


14.4 


124 


51.1 


190 


87.8 


251, 


124.4 


322 


161.1 




360. 


— 7 


-21.7 


59 


15. 


125 


51.7 


191 


88.3 


257 


125. 


323 


161.7 


690 


365.6 


— 6 


-21.1 


60 


15.6 


126 


52.2 


192 


88.9 


25'- 


125.6 


324 


162.2 


700 


371.1 


— 5 


-20.6 


61 


16.1 


127 


52.8 


19? 


89.4 


259 


126.1 


■•- 


162.8 


710 


376.7 


- 4' 


-20. 


62 


16.7 


128 


53.3 


194 


90. 


261 


126.7 


-. 


163.3 


720 


382.2 


- 3 


—10.4 


C3 


17.2 


129 


53.9 


195 


90.6 


261 


127.2 


■ - 


163.9 


730 387.8 


- 2 


-18.9 


64 


17.8 


130 


54.4 


196 


91.1 


262 


127.8 


.- :■ 


164.4 


740 


393.3 


- 1 


—18 3 


65 


18.3 


131 


55. 


197 


91.7 


263 


128.3 


829 


165. 


750 


398.9 





-17.8 


66 


18.9 


132 


55.6 


\9r 


92.2 


264 


128.9 


330 


165.6 


760 


404.4 


+ 1 


—17.2 


67 


19.4 


133 


56.1 


199 


92.8 


265 


129.4 


331 


166.1 


770 


410. 


2 


-16.7 


68 


20. 


134 


56.7 


20!" 


93.3 


266 


130. 


- - 


166.7 


780 


415.6 


3 


-16.1 


63 


20.6 


135 


57.2 


201 


93.9 


207 


130.6 


;>: 


167.2 


790 


421.1 


4 


—15.6 


70 


21.1 


136 


57 8 


202 


94. 4 


.' 


131.1 


334 


167.8 


SOO 


426.7 


5 


-15. 


71 


21.7 


137 


58.3 


203 


95. 


269 


131.7 


335 


168.3 


810 


432.2 


6 


—14.4 


72 


22.2 


138 


58.9 


204 


95.6 


270 


132.2 


336 


168.9 


820 


437.8 


7 


-13.9 


73 


22.8 


139 


59.4 


205 


96.1 


271 


132.8 


337 


169.4 


830 


443.3 


8 


—13.3 


74 


23.3 


140 


60. 


206 


96.7 


272 


133.3 


338 


170. 


840 


448.9 


9 


—12.8 


75 


23.9 


141 


60.6 


207 


97.2 


273 


133.9 


222; 


170.6 


8.50 


454.4 


10 


-12.2 


76 


24.4 


142 


61.1 


208 


97.8 


274 


134.4 


340 


171.1 


860 


460. 


11 


-11.7 


77 


25. 


143 


61.7 


209 


98.3 




135. 


341 


171.7 


870 


465.6 


12 


—11.1 


78 


25.6 


144 


62.2 


210 


98.9 


270 


135.6 


342 


172.2 


880 


471.1 


13 


-10.6 


79 


26.1 


145 


62.8 


211 


99 4 




136.1 


: -, 


172.8 


890 


476.7 


14 


-10. 


80 


26.7 


146 


63.3 


212 


100. 




136.7 


344 


173.3 


900 


482.2 


15 


— 9.4 


81 


27.2 


147 


63.9 


213 


100.0 


279 


137.2 


345 


173.9 


910 


487.8 


16 


— 8.9 


82 


27.8 


148 


64.4 


214 


101.1 




137.8 


346 


174.4 


920 


493.3 


17 


— 8.3 


83 


28.3 


149 


65. 


215 


101.7 




138.3 


347 


175. 


930 


498.9 


18 


— 7.8 


84 


28.9 


150 


65.6 


216 


102.2 




138.9 


348 


175.6 


940 


504.4 


19 


— 7.2 


85 


29.4 


151 


66.1 


217 


102.8 


222 


139.4 


349 


176.1 


950 


510; 


20 


— 6.7 


86 


30. 


152 


66.7 




103.3 


284 


140. 


350 


176.7 




515.6 


21 


— 6.1 


87 


30.6 


153 


67.2 


219 


103.9 


285 


140.6 


351 


177.2 


970 


521.1 


22 


- 5.6 


88 


31.1 


154 


67.8 




104.4 


286 


141.1 




177.8 


980 


526.7 


23 


— 5. 


89 


31.7 


155 


68.3 


221 


105. 




141.7 


353 


178.3 


990 


532.2 


24 


- 4.4 


90 


32.2 


156 


68.9 




105.6 




142.2 


354 


178.9 


1000 


537.8 


25 


t- 3.9 


91 


32.8 


157 


69.4 




106.1 




142.8 


355 


179.4 


1010 543.3 



USEFUL TABLES. 



DECIMALS OF A. FOOT FOR EACH & OF 
AN INCH. 



Inch. 


o" 


1" 


2" 


3" 


4" 


5" 








.0833 


.1667 


2500 


3333 


4167 


i 


.0013 
0026 
.0039 
.0052 


.0848 
.0859 
.0872 
.0885 


.1680 
.1693 
.1708 
• 1719 


.2513 
.2526 
.2539 
.2552 


.3346 
.3359 
.3372 
.3385 


.4180 
.4193 
.4206 
.4219 


'A 

i 

i 


0085 
.0078 
.0091 
.0104, 


.0898 
.0911 
.0924 
.0937 


.1732 
.1745 
.1758 
.1771 


.2565 
.2578 
.2591 
.2604 


.3398 
.3411 
.3424 
.3437 


.4232 
.4245 
.4258 
.4271 


A 
A 

8 


.0117 
.0130 
.0143 
.0156 


.0951 
.0984 
.0977 
.0990 


.1784 
.1797 
1810 
.1823 


.2617 
.2630 
.2643 
.2656 


3451 
.3464 
.3477 
.3490 


.4284 
.4297 
.4310 
.4323 




.0169 
.0182 
0195 
.0208 


.1003 
.1016 
.1029 
.1042 


.1836 
.1849 
.1862 
.1875 


.2669 
.2682 
.2695 
.2708 


.3503 
.3516 
.3529 
.3542 


.4336 
.4349 
.4362 
.4375 


if 


.0221 
.0234 
.0247 
.0260 


.1055 
.1038 
.1081 
.1094 


.1888 
.1901 
.1914 
.1927 


.2721 
.2734 
,2747 
.2760 


.3555 
.3568 
.3581 
.3594 


.4388 
.4401 
.4414 
.4427 


If 

1 


.0273 
.0286 
.0299 
0312 


.1107 
.1120 
.1133 
.1146 


.1940 
.1953 
.1966 
.1979 


.2773 
.2786 
.2799 
.2812 


.3607 
.3620 
.3633 
.3646 


.4440 
.4453 
.4466 
.4479 


11 
1 


.0326 
.0339 
0352 
.0365 


.1159 
.1172 
.1185 
.1198 


.1992 
.2005 
2018 
.2031 


.2826 
.2839 
.2852 
.2865 


.3659 
3672 
3685 
.3698 


.4492 
.4505 
.4518 
.4531 


* 


.0378 
0391 
.0404 
.0417 


.1211 
.1224 
.1237 
.1250 


.2044 
•2057 
.2070 
.2083 


.2878 
.2891 
.2904 
.2917 


.3711 
.3724 
.3737 
.3750 


.4544 
.4557 
.4570 
.4583 



USEFUL TABIDS. 



203 



DECIMALS OP A FOOT FOR EACH ^ OF 
AN INCH 



Inch. 


*6" 


7" 


8' 


P-" 


10" 


U" 





5000 


5833 


.6667 


7500 


.8333 


9167 


<h 


6013 


5846 


.6680 


.7513 


.8346 


.9180 


A 


.5026 


5859 


6693 


.7526 


.8359 


.9193 


A 


.5039 


5872 


.6706 


.7539 


8372 


.9206 


A 


.5052 


.6885 


.6719 


.7552 


.8385 


.9219 


A 


.5065 


.5898 


.6732 


.7565 


.8398 


.9232 


& 


.5078 


5911 


.6745 


.7578 


.8411 


.9245 


A 


.5091 


.5924 


.6758 


7591 


.8424 


.9258 


i 


5104 


5937 


.6771 


.7604 


.8437 


,9271 


A 


.5117 


.6951 


.6784 


.7617 


.8451 


.9284 


A 


.6130 


.5964 


.6797 


.7630 


.8464 


.9297 


H 


•5143 


.5977 


.6810 


.7643 


.8477 


.9310 


A 


.5156 


.5990 


.6823 


.7656 


.8490 


.9323 


H 


.5169 


.6003 


.6838 


7669 


.8503 


.9336 


A 


5182 


.6016 


.6849 


.7682 


.8516 


.9349 


if 


5195 


.6029 


.6862 


.7695 


.8529 


.9362 


1 


.5208 


.6042 


.6875 


.7708 


.8542 


.9375 


tf 


.5221 


.6055 


.6888 


.7721 


.8555 


.9388 


A 


.5234 


6068 


.8901 


.7734 


.8568 


.9401 


If 


.5247 


.6081 


.6914 


.7747 


.8581 


.9414 


A 


.5260 


.6094 


.6927 


.7760 


.8594 


.9427 


ft 


.5273 


.6107 


.6940 


.7773 


.8607 


.9440 


H 


.5286 


.6120 


.6953 


.7786 


.8620 


.9453 


** 


.5299 


.6133 


.6966 


.7799 


.8633 


.9466 


t 


.5312 


.6146 


.6979 


.7812 


.8646 


.9479 


ft 


.5326 


.6159 


.6992 


.7826 


.8669 


.9492 


tt 


.5339 


.6172 


.7005 


.7839 


.8672 


.9505 


¥ 


.5352 


.6185 


.7018 


.7852 


.8685 


.9518 


A 


.5365 


.6198 


.7031 


.7865 


.8698 


9531 


H 


.5378 


.6211 


.7044 


.7878 


.8711 


.9544 


« 


.5391 


.6224 


.7057 


.7891 


.8724 


.9557 


¥ 


.5404 


.6237 


.7070 


.7904 


.8737 


.9570 


i 


.5417 


6250 


.7083 


.7917 


.8750 


.9583 



204 



USEFUL TABLES. 



DECIMALS OF A FOOT FOR EACH & OF 
AN INCH. 



Inch. 





1" 


2" 


3" 


4" 


5" 


« 

s 


.0430 
.0443 
.0456 
.0409 


.1263 
.1276 
.1289 
.1302 


.2096 
.2109 
.2122 
.2135 


.2930 
.2943 
.2956 
.2969 


.3763 
.3776 
.3789 
.3802 


,4596 
.4609 
.4622 
.4635 


If 


.0482 
.0495 
.0508 
.0521 


.1315 
.1328 
.1341 
.1354 


.2148 
.2101 
.2174 
.2188 


.2982 
.2995 
.3008 
,3021 


.3815 
.3828 
.3841 
.3854 


.4648 
.4661 
.4674 
.4688 


ft 

H 

II 


.0534 
.0547 
.0500 
.0573 


.1367 
.1380 
.1393 
.1406 


.2201 
.2214 
.2227 
.2240 


.3034 
.3047 
.3060 
.3073 


.3867 
.3880 
.3893 
.3903 


.4701 
.4714 
.4727 
.4740 


If 

I 


.0586 
.0599 
.0012 
.0625 


.1419 
.1432 
.1445 
.1458 


.2253 
.226*? 
.2279 
.2292 


.3088 
.3099 
.3112 
.3125 


.3919 
.3932 
.3945 
.3958 


.4753 
.4766 
.4779 
.4792 


ft 
If 


.0838 
.0051 
.0004 
.0677 


.1471 
.1484 
.1497 
.1510 


.2305 
.2318 
.2331 
.2344 


.3138 
.3151 
.3164 
.8177 


.3971 
.3984 
.3997 
.4010 


.4805 
.4818 
.4831 
.4844 


ft 

1 


.0690 
.0703 
.0716 
.0729 


.1523 
.1536 
.1549 
.1502 


.2357 
.2370 
.2383 
2396 


.3190 
.3203 
.3216 
.3229 


.4023 
.4036 
.4049 
•4062 


.4857 
.4870 
.4883 
•4896 


ft 

If 

If 
it 


.0742 
.0755 
.0768 
.0781 


.1576 
.1589 
.1602 
.1615 


.2409 
.2422 
.2435 
.2448 


.3242 
.8255 
.3268 
.3281 


.4070 
.4089 
.4102 
.4115 


.4909 
.4922 
.4935 
.4948 


ft 
ft 

f 


.0794 
.0807 
.0820 


.1628 
1641 
.1054 


.2461 
.2474 
.2487 


.3294 
.3307 
.3320 


.4128 
.4141 
.4154 


.4961 
.4974 
.4987 



USEFUL TABLES. 



205 



DECIMALS OF A FOOT FOR EACH & OF 
AN INCH. 



Inoh. 


6" 


7" 


8" 


9" 


10" 


11" 


If 
H 
fl 
A 


.5430 
5443 
.5456 
.5469 


.6263 
.6276 
.6289 
.6302 


.7096 
.7109 
.7122 
.7135 


.7930 
.7943 
.7956 
.7969 


.8763 
.8776 
.8789 
.8802 


.9596 
.9609 
.9622 
.9635 




5482 
5495 
5508 
.5521 


.6315 
.6328 
.6341 
.6354 


.7148 
.7161 
•7174 
.7188 


.7982 
.7995 
8008 
.8021 


.8815 
.8828 
.8841 
.8854 


9648 
.9661 
.9674 
.9688 


It 


.5534 

.5547 
5560 
5573 


6367 
.6380 
.6393 
.6408 


7201 
.7214 
.7227 
.7240 


.8034 
.8047 
.8060 
8073 


.8867 
.8880 
8893 
.8906 


.9701 
.9714 
.9727 
.9740 


II 

23 
32 

1 


.5586 
5599 
.5612 
.5625 


6419 
6432 
.6445 
.6458 


.7253 
7266 

.7279 
.7292 


.8086 
.8099 
8112 
8125 


.8919 
.8932 
8945 
8958 


.9753 
9766 
9779 
9792 


25 
32 
51 
61 

11 


5638 
5651 
5664 
5677 


6471 
.6484 
.6497 
6510 


.7305 
.7318 
.7331 
.7344 


.8138 
.8151 
8164 
.8177 


8971 
.8984 
.8997 
.9010 


.9805 
.9818 
9831 
.9844 


If 

H 

f 


.5690 
.5703 
5716 
.5729 


.6523 
.6536 
.6549 
.6562 


.7357 
.7370 
.7383 
.7396 


.8190 
.8203 
.8216 
.8229 


9023 
.9036 
9049 
.9062 


9857 
.9870 
9883 
9896 


5.7. 

6? 
29 
32 

M 

15 


.5742 
.5755 
.5768 
.5781 


.6576 
.6589 
.6602 
.6615 


.7409 
.7422 
.7435 
.7448 


.8242 
.8255 
.8268 
.8281 


.9076 
.9089 
.9102 
9115 


.9909 
.9922 
.9935 
•9948 


n 

31 
32 

tt 

1 


5794 
5807 
.5820 


.6628 
.6641 
G654 


.7461 
.7474 
.7487 


.8294 
.8307 
.8320 


.9128 
.9141 
.9154 


.9961 

.9974 

.9987 

1.0000 



206 



USEFUI, TABLES. 



DECIMALS OP AN INCH FOR EACH ^fth. 



■g^ds. 


^ths. 


Decimal. 


Fraction 


•g^ds. 


B^ths. 


Decimal. 


Fraction 




1 


.015625 






33 


.515625 




1 


2 


.03125 




17 


34 


.53125 






3 


.046875 






35 


.546875 




2 


4 


.0625 


1-16 


18 


36 


.5625 


9-16 




5 


.078125 






37 


.578125 




3 


6 


.09375 




19 


38 


.59375 






7 


.109375 






39 


.609375 




4 


8 


.125 


1-8 


20 


40 


.625 


5-8 




9 


.140625 






41 


.640625 




5 


10 


.15625 




21 


42 


.65625 






11 


.171875 






43 


.671875 




6 


12 


.1875 


3-16 


22 


44 


.6875 


11-16 




13 


.203125 






45 


.703125 




7 


14 


.21875 




23 


46 


.71875 






15 


.234375 






47 


.734375 




8 


16 


.25 


1-4 


24 


48 


.75 


3-4 




17 


.265626 






49 


.765625 




9 


18 


.28125 




25 


50 


.78125 






19 


.296875 






51 


.796875 




10 


20 


.3125 


5-16 


26 


52 


.8125 


13-16 




21 


.328125 






53 


.828125 




11 


22 


.34375 




27 


54 


.84375 






23 


.359375 






55 


.859375 




12 


24 


.375 


3-8 


28 


56 


.875 


7-8 




25 


.390625 






57 


.890625 




13 


26 


.40625 




29 


58 


.90625 






27 


.421875 






59 


.921875 




14 


28 


.4375 


7-16 


30 


60 


.9375 


15-16 




29 


.453125 






61 


.953125 




15 


30 


.46875 




31 


62 


.96875 






31 


.484375 






63 


.984375 




16 


32 


.5 


1-2 


32 


64 


1. 


1 



USEFUL TABLES. 



207 



TABLES FOR CALCULATING THE HORSE POWER 
OF WATER. 





MINERS' INCH TABLE. 




CUBIC FEET TABLE. 


The following table gives 


the Horse- 


The following table gives the Horse- 


Power of one miner's inch of water un- 


Powe 


r of one cubic foot of water pe» 


der heads from one up to e 


even huu- 


minute under heads from one up to 


dred feet. This in 


:h equals 


i>2 cubic 


eleven hundred feet. 




feet per minute. 














Heads 
in Feet. 


Horse Power 


in Feet. 


Horse Power. 


Heads 
in Feet. 


Horsepower. 


in Feet. 


Horse Power. 


1 


.0024147 


320 


.772704 


1 


.0016098 


320 


.515136 


20 


.0482294 


330 


.796851 


20 


.032196 


330 


.531234 


30 


.072441 


340 


.820998 


30 


.048294 


340 


.547332 


40 


.090588 


350 


.845145 


40 


.064392 


350 


.563430 


50 


.120735 


360 


.869292 


50 


.080490 


360 


.579528 




.144S82 


370 


.898439 


60 


.096588 


370 


.595626 


70 


.169029 


380 


.917586 


70 


.112686 


380 


.611724 


SO 


.193176 


390 


.941733 


80 


.128784 


390 


.627822 


90 


.217323 


400 


.965S80 


90 


.144892 


400 


.643920 


100 


.241470 


410 


.990027 


100 


.160980 


410 


.660018 


110 


.265617 


420 


1.014174 


110 


.177078 


420 


.676116 


120 


.289764 


430 


1.038321 


120 


.193173 


430 


.692214 


130 


.313911 


440 


1.062468 


130 


.209274 


440 


.708312 


140 


.338058 


450 


1.0S6615 


140 


.225372 


450 


.724410 


150 


.362205 


460 


1.110762 


150 


.241470 


460 


.740503 


160 


.386352 


470 


1.134909 


160 


.257568 


470 


.756606 


170 


.410499 


480 


1.159056 


170 


.273666 


480 


.772704 


180 


.434646 


490 


1.183206 


180 


.289764 


490 


.788802 


190 


.458793 


500 


1.207350 


190 


.305862 


500 


.804900 


200 


.482940 


520 


1.255644 


200 


.321960 


520 


.837096 


210 


.507087 


540 


1.303938 


210 


.338058 


540 


.869292 


220 


.531234 


560 


1.352232 


220 


.354156 


560 


.90148? 


230 


.555381 


580 


1.400526 


230 


.370254 


580 


.933684 


240 


.579528 


600 


1.44«820 


240 


.386352 


600 


.965880 


250 


.603675 


650 


1.569555 


250 


.402450 


650 


1.046370 


260 


.627822 


700 


1.690290 


260 


.418548 


700 


1.126860 


270 


.651969 


750 


1.811025 


270 


.434646 


750 


1.207350 


280 


.676116 


800 


1.931760 


280 


.450744 


800 


1.287840 


290 


.700263 


900 


2.173230 


290 


.466842 


900 


1.448820 


300 


.724410 


1000 


2.414700 


SCO 


.482940 


1000 


1.609800 


310 


.748557 


1100 


2.656170 


310 


.499038 


1100 


1.770780 



WHEN THE EXACT HEAD IS FOUND IN ABOVE TABLE. 

Example. — Have 100 foot head and 50 inches of water. How many Horse- 
Power? 

By reference to above table the Horse Power of 1 inch under 100 ft. head 
is .241470. This amount multiplied by the number of inches. 50, will give 12.07 
Horse Power. 

WHEN EXACT HEAD IS NOT FOUND IN TABLE. 

Take the Horse Power of 1 inch under 1 ft. head and multiply by the num- 
ber of inches, and then by number of feet head. The product will be the required 
Horse Power. 

The above formula will answer for the cubic feet table, by substituting the 
the equivalents therein for those of miner's inches. 

Note. — The above tables are based upon an efficiency of 85%. 



208 



USKFUI. TABLES. 



LOSS OF HEAD IN PIPE BY FRICTION. 

The following tables show the loss of head by friction in each 100 feet in length of different 
diameters of pipe when discharging the following quantities of water per minute: 

INSIDE DIAMETER OF PIPE IN INCHES. 



1 


2 


3 


4 


5 


6 


Vein 


Loss of 


Cubic 


Loss of 


Cublo 


Loss of 


Cubic 


Loss of 


Cubic 


Loss of 


Cubic 


Lose of 


Cubic 






feet 




feet 


head 










feet 




feet 


per 


In 


ppx 


in 




in 




in 




in 


per 


in 






feet. 




feet. 


mln. 


feet 


min. 


feet. 


min. 


feet. 




feet. 


min. 


2.0 


2.87 


.65 


1.185 


2.62 


.791 


5.89 


.593 


10.4 


.474 


16.3 


.395 


23.5 


2.2 


2.80 


.73 


1.404 


2.88 


.936 


0.48 


.702 


11.5 


.561 


18. 


.408 


25.9 


2.4 


3.27 


.79 


1.639 


3.14 


1.093 


7.07 


.819 


12.5 


.050 


19.6 


.547 


28.2 


2.0 


3.78 


.86 


1.891 


3.40 


1.26 


7.05 


.945 


13.6 


.757 


21.3 


.631 


30.6 


28 


4.32 


.92 


2.16 


3.66 


1.44 


8.24 


1.08t 


14.6 


.864 


22.9 


.720 


32.9 


8.0 


4.89 


.99 


2.44 


3.92 


1.62 


8.83 


1.22 


15.7 


.978 


24.6 


.815 


35.3 


S.2 


5.47 


1.06 


2.73 


4.18 


1.82 


9.42 


1,37 


16.7 


1.098 


26.2 


.915 


37.7 


S.4 


6.09 


1.12 


3.05 


4.45 


2.04, 


10.00 


1.52 


17.8 


1.22 


27.8 


1.021 


40. 


3.6 


6.76 


1.19 


3.38 


4.71 


2.26 


10.60 


1.69 


18.8 


1.35 


29.4 


1.131 


42.4 


3.8 


7.48 


1.20 


3.74 


4.97. . 


2.49. 


11.20 


1.87 


19.9 


1.49 


31. 


1.25 


44.7 


4.0 


8.20 


1.32 


4.10 


5.23 


2.73 


11.80 


2.05 


20.9 


1.64 


32.7 


lv37 


47.1 


4.2 


8.97 


1.39 


4.49 


5.49 


2.98 


12.30 


2.24 


22.0 


1.79 


34.3 


1.49 


49.5 


4.4 


9.77 


1.45 


4.89 


5.76 


3.25 


12.90 


2.43 


23.0 


1.95 


36.0 


1.02 


51.8 


4.0 


10.00 


1.52 


5.30 


6.02 


3.53 


■13.50 


2.64 


24.0 


2.11 


37.6 


1.76 


54.1 


4.8 


11.46 


1.58 


5.72 


6.28 


3:81 


14.10 


2.85- 


25.1 


2.27 


39.2 


1:90 


56.5 


6.0 


12.33 


1.65 


6.17 


6.54 


4.11 


14.70 


3.08 


26.2 


2.46 


40.9 


2.05 


58.9 


6.2 


13.24 


1.72 


0.02 


6.80 


4.41 


15.30 


3*31 


27.2 


2.65 


42.5 


2.21 


61.2 


6.4 


14.20 


1.78 


7.10 


7.00 


4.73 


15.90 


3.55 


28.2 


2.84 


44.2 


2.37 


63.6 


6.0 


16.16 


1.85 


7.58 


7.32 


5.06 


10.50 


3.79 


29.3 


3.03 


45.8 


2.53 


65.9 


6.8 


10.17 


1.91 


8.09 


7.58 


5.40 


17.10 


4.04 


30.3 


3.24 


47.4 


2.70 


68.3 


6.0 


17.23 




8.01 


7.85 


5.74 


17.70 


4.31 


31.4 


3.45 


49.1 


2.87 


70.7 


7.0 


22.89 


2k 


11.46 


9.16 


7.62 


20.6 


5.72 


30.6 


4.57 


57.2 


3.81 


82.4 



INSIDE DIAMETER OF PIPE IN INCHES. 



7 


8 


9 


10 


11 


12 


Velo 


Loss of 


Cubic 


Loss of 


Cubic 


Loss of 


Cubic 


Loss of 


Cubic 


Loss of 


Cubio 


Loss of 


Cubic 


In ft. 




feet 




feet 


head 


feet 




feet 




feet 




feet 




in 


per 




per 




per 




per 




per 






sec. 


feet. 




feet. 


min. 


feet. 


min. 


feet. 


min. 


feet. 




feet. 


mm. 


2.0 


.338 


32.0 


.296 


41.9 


.264 


53. 


.237 


05.4 


.210 


79.2 


.198 


94.2 


2.2 


.401 


35.3 


.351 


46.1 


.312 


58.3 


.281 


72. 


.255 


87.1 


.234 


103. 


2.4 


.408 


38.5 


.410 


60.2 


.365 


63.6 


.327 


78,5 


.297 


95.0 


.273 


113. 


2.6 


.540 


41.7 


.473 


54.4 


.420 


68.9 


.378 


85.1 


.344 


103*. 


.315 


122. 


2.8 


.617 


449 


.540 


58.6 


.480 


74.2 
79.5 


.432 


91.0 


.392 


111. 


.360 


132. 


3.0 


.098 


43.1 


.611 


62.8 


.544 


.488 


98.2 


.444 


119. 


.407 


141. 


3.2 


.785 


61.3 


.686 


67'. 


.609 


84.8 


.549 


105. 


.499 


127. 


.457 


151. 


3.4 


.876 


54.5 


.765 


71.2 


.680 


90.1 


.612 


111. 


.557 


134. 


.510 


160. 


3.0 


.969 


57.7 


.848 


75.4 


.755 


95.4 


.679 


118. 


.017 


142. 


.566 


169. 


8.8 


lfi70 


60.9 


.936 


79.0 


.831 


101. 


.749 


124. 


.080 


150. 


.624 


179. 


4.0 


1.175 


C4.1 


1.027 


83.7 


:913 


106. 


.822 


131. 


.747 


158. 


.685 


188. 


4.2 


1.28 


07.3 


1,122 


87.9 


.998 


111. 


.897 


137. 


.810 


166. 


.749 


198. 


4.4 


1.39 


70.5 


1.22 


92,1 


1.086 


116. 


.977 


144. 


.888 


174. 


.815 


207. 


4.0 


1.51 


73.7 


1.32 


96.3 


1.177 


122. 


1.059 


150. 


.903 


182, 


.883 


217. 


4.8 


a.63 


70.9 


1.43 


100.0 


1.27 


127. 


1.145 


167. 


1.040 


190. 


.954 


226 


6.0 


1.76 


80.2 


1.54 


105. 


1.37 


132. 


1.23 


163. 


1.122 


198. 


1.028 


235. 


6.2 


1.89 


83.3 


1.65 


109. 


1.47 


138. 


1.32 


170. 


1.20 


206. 


1.104 


245 


6.4 


2.03 


80.0 


1.77 


113. 


1.57 


143. 


1.41 


177. 


1.28 


214. 


1.183 


254. 


6.0 


2.17 


89.8 


1.89 


117. 


1.08 


148. 


1.51 


183. 


1.37 


222. 


1.26 


264. 


5.8 


2.31 




2.01 


121. 


1.80 


154. 


1.61 


190. 


1.46 


229. 


134 


273. 


6.0 


2.4S 


96^2 


2.15 


125. 


1.92 


159. 


1.71 


196. 


1.56 


237. 


1.43 


283. 


7.0 


3.20 


112.0 


2.S5 


140. 


2.52 


185. 


2.28 


229. 


2.07 


277. 


1.91 


330. 



USEFUL TABLES. 



209 



LOSS OF HEAD IN PIPE BY FRICTION. 

The following tables show the loss of head by friction in each 100 feet in length of different 
diameters of pipe when discharging the following quantities of water per inipute: 

INSIDE DIAMETKR OF PIPE IN INCHES. 





13 


14 


15 


16 


18 


20 




Loss of 


Cubic 


Loss of 


Cubic 


Loss of 


Cubic 


Loss of 


Cubic 


Loss of 


Cubic 


Loss of 


Cubic 


In ft. 




feet 




feet 




feet 




feet 




reet 




feet 




In 








In 


















feet. 




feet. 




feet. 




feet. 


mln. 


feet. 






mm. 


2.0 


.183 


110. 


.169 


128. 


.158 


147. 


.147 


167. 


.132 


212. 


.119 


262. 


2.2 


.216 


J21. 


.200 


141. 


.187 


162. 


.175 


184. 


.156 


233. 


.140 




2.4 


.252 


133. 


.234 


154. 


.218 


176. 


.205 


201. 


.182 


254. 


.164 


314. 


2.6 


.290 


144. 


.270 


167. 


.252 


191. 


.236 


218. 


.210 


275. 


.189 


340. 


2.8 


.332 


156. 


.308 


179. 


.288 


206. 


,270 


234. 


.240 


297. 


.216 


366. 


8.0 


.375 


166. 


.349 


192. 


.325 


221. 


.306 


251. 


.271 


318. 


.245 


393. 


3.2 


.422 


177. 


.392 


205. 


.366 


235. 


.343 




.305 


339. 


.275 


419. 


3.4 


.471 


188. 


438 


218. 


.408 


250. 


.383 


284. 


.339 


360. 


.306 


445. 


J.6 


.522 


199. 


.485 


231. 


.452 


265. 


.425 


301. 


.377 


382. 


.339 


471. 


3.8 


.576 


210. 


.535 


243. 


.499 


280. 


.468 


318. 


.416 


403, 


.374 


497. 


4.0 


.632 


221. 


.587 


256. 


.543 


294. 


.513 


335. 


.456 


424. 


.410 


523. 


4.2 


.691 


232. 


.641 




.598 


309. 


.561 


352. 


.499 


445. 


.449 


550. 


4.4 


.751 


243. 


.698 


282. 


.651 


324. 


.611 


368. 


.542 


466. 


.488 


576. 


4.6 


.815 


254. 


.757 


295. 


.707 


339. 


.662 


385. 


.588 


488. 


.529 


602. 


4.8 


.881 


265. 


.818 


308. 


.763. 


353. 


.715 


402. 


.636 


509. 


.572 


628. 


6.0 


.949 


276. 


.881 


321. 


.822 


363. 


.770 


419. 


.685 


530. 


.617 


654. 


5.2 


1.020 


287. 


.947 


833. 


.883 




.828 


435. 


.736 


551. 


.662 


680. 


5.4 


1.092 


298. 


1.014 


346. 


.947 


397. 


.888 


452. 


.788 


572. 


.710 


707. 


5.6 


1.167 


309. 


1.083 


359. 


1.011 


412. 


.949 


169. 


.843 


594. 


.758 


733. 


5.8 


1.245 


821. 


1.155 


372. 


1078 


427. 


1.011 


486. 


.899 


615. 


.809 


759.- 


fi.0 


1.325 


332. 


1.229 


385. 


1.148 


442. 


1.076 


502. 


.957 


636. 


.861 


785. 


7.0 


1.75 


387. 


1.63 


449. 


1.52 


515. 


1.43 


586. 


1.27 


742. 


1.143 


916. 



INSIDE DIAMETER OF PIPE IN INCHES. 





22 


21 


26 


28 


30 


36 


Vein. 


Loss of 


Cubic 


Loss of 


Cubic 


Loss of 


Cubic 


Loss of 


Cubic 


Loss of 


Cubic 


I.OSSOf 


cubic 




heud 


feet 




feet 








feet 




feet 




feet 


PIT 






In 




in 




in 




in 








sec. 


feet. 




feet. 


mm. 


feet. 




feet. 




feet. 


mln. 






2.0 


.108 


316 


.098 


377. 


.091 


44? 


.084 


513. 


.079 


5S9. 


.0(56 


848. 


22 


.127 


348 


.116 


414. 


.108 


486 


.099 


564. 


.093" 


648. 






2.4 


.149 


380 


.136 


452. 


.126 


531 


.116 


616. 


.109 


707. 


.091 


1018. 


2.6 


.171 


412 


.157 


490. 


.145 


575 


.134 


667. 


.126 


766. 


.104 


1100. 


2.8 


.195 


443 


.180 


528. 


.165 


619 


.153 


718. 


.144 


824. 


.119 


1183. 


3.0 


.222 


475 


.204 


565. 


.188 


663 


.174 


770. 


.163 


883. 


.135 


1273. 


3.2 


.249 


507 


.229 


603. 


.211 


70S 


.195 


821. 


.182 


942. 


.152 


1357. 


3.4 


.273 


538 


. .255 


641. 


.235 


75? 


.218 


872. 


.204 


1C01. 


.169 


1442. 


3.6 


.308 


570 


.283 




.261 


796 


.242 


923. 


.226 


1060. 


.188 


1527. 


3.8 


.340 


601 


.312 


716. 


.288 


840 


.267 


974. 


.249 


1119. 


.207 


1612. 


4.0 


.373 


633 


.342 


754. 


.315 


885 


.293 


1026. 


.273 


1178. 


.228 


1697. 


4.2 


.408 


665 


.374 


791. 


.345 


9V!9 


.320 


1077. 


.299 


1237. 


.249 


1782. 


4.4 


.444 


697 


.407 


829. 


.375 


973 




1129. 


.325 


1296. 


.271 


1866. 


4.6 


.482 


728 


.441 


867. 


.407 


1017 


.378 


1180. 


.353 


1355. 


.294 


1951 


4.8 


.521 


760 
792 


.476 


905. 


.440 


106? 


.409 


1231. 


Ml 


1414. 


.318 


2036. 


5.0 


.561 


.513 


942. 


.474 


llOfl 


.440 


1283. 


.411 


1472. 


.312 


212L 


5.2 


.602 


823 


.552 


980. 


.510 


1150 


.473 


1334. 


.441 


1531. 


.368 


2206.. 


5.4 


.645 


855 


.591 


1018: 


.546 


1194 


.507 


1885. 


.473 


1590. 


.394 


2291. 


5.6 


.690 


887 


.632 


1055. 


.683 


1?39 


.542 


1437. 


.506 


1649. 


.421 


2376. 


5.8 


.735 


yi8 


.674 


1093. 


.622 


19183 


.578 


1488. 


.540 


1708. 


.450 


2460. 


6.0 


.782 


950 


.717 


1131. 


.662 


1327 


.615 


1539. 


.574 


1767. 


.479 


2545. 


7.0 


1.040 


J 109 


.953 


1319. 


.879 


1548 


.817 


1796. 


.762 


2061. 


.636 


2858. 



USKFUIv TABLES. 



TABLE OF SHEET IRON HYDRAULIC PIPE. 



i 

© . 


3- 


la, 


if 


f hi 


~£ 
















S-= 


£* 


-* . 


sfS'gp. 


r* 


s.g 


^2 


££ 


So-3 


§f££ 


£is 


3 


7 


18 


400 


9 


2 


4 


12 


18 


350 


16 


2* 


4 


12 


16 


525 


16 


3 


5 


20 


18 


325 


25 


3* 


o 


20 


16 


500 


25 


4} 


o 


20 


14 


675 


25 


5 


a 


28 


18 


296 


36 


4| 


6 


28 


16 


487 


36 


6* 


6 


28 


14 


743 


36 


7} 




38 


18 


254 


50 


5} 


7 


38 


16 


419 


50 


6* 


7 


38 


14 


640 


50 


8} 


8 


50 


16 


367 


63 


7* 


8 


50 


14 


560 


63 


9h 


8 


50 


12 


854 


63 


13 


y 


63 


16 


327 


80 


8* 


!) 


63 


14 


499 


80 


10£ 


9 


63 


12 


761 


80 


14* 


10 


78 


16 


295 


100 


9* 


so 


78 


14 


450 


100 


in 


10 


78 


12 


687 


100 


15f 


10 


78 


11 


754 


100 


17* 


10 


78 


10 


900 


100 


19} 


11 


95 


16 


269 


120 


n 


11 


95 


14 


412 


120 


13 


11 


95 


12 


626 


120 


17* 


11 


95 


11 


687 


120 


18jf 


11 


95 


10 


820 


120 


' 21 


12 


113 


16 


246 


142 


in 


12 


113 


14 


377 


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14 


12 


113 


12 


574 


142 


18} 


12 


113 


11 


630 


142 


19| 


12 


113 


10 
16 


753 


142 


22| 


13 


132 


228 


170 


12 


13 


132 


14 


348 


170 


15 


13 


132 


12 


530 


170 


20 


13 


132 


11 


583 


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22 


13 


132 


10 


696 


170 


24} 


14 


153 


16 


211 


200 


13 


14 


153 


14 


324 


200 


16 


14 


153 


12 


494 


200 


214 


14 


153 


11 


543 


200 


23* 


14 


153 


10 


648 


200 


*6 


15 


176 


16 


197 


225 


13f 


15 


176 


14 


302 


225 


17 


15 


176 


12 


460 


225 


23 


15 


176 


11 


507 


225 


24* 


15 


176 


10 


606 


225 


28 


16 


201 


16 


185 


255 


14* 


16 


201 


14 


283 


255 


17* 


46 


201 


12 


432 


255 


24* 


16 


201 


11 


474 


255 


26* 


i£ 


I 201 


10 


567 


255. 


29J 



|| 
£.5 


& 

p. 

If 


is 


P 

ill 

K5.TS 


•°.seS 




18 


254 


16 


165 


320 


16* 


18 


254 


14 


252 


320 


20* 


18 


254. 


12 


385 


320 


2;* 


18 


254 


11 


424 


320 


30 


,18 


254 


10 


505 


320 


34 


20 


314 


16 


148 


400 


18 


20 


314 


14 


227 


400 


22} 


20 


314 


12 


346 


400 


30 


20 


314 


11 


380 


400 


324 


20 


314 


10 
"16 


456 
135" 


400 
4«0 


36} 


n 


380 


20 


22 


380 


14 


206 


480 


m 


22 


380 


12 


316 


480 


32$ 


22 


380 


H 


347 


480 


35$ 


22 


380 


10 


415 


480 


40 


24 


452 


14 


188 


570 


27* 


24 


452 


12 


290 


570 


35* 


24 


452 


11 


318 


570 


39 


24 


452 


10 


379 


570 


43* 


24 


452 


8 


466 


570 


53 


26 


530 


14 


175 


670 


29* 


26 


530 


12 


267 


670 


38* 


26 


530 


11 


294 


670 


42 


26 


530 


10 


352 


670 


47 


26 


530 


8 


432 


670 


57* 


28 


615 


14 


102 


775 


31* 


28 


615 


12 


247 


775 


41* 


28 


615 


11 


273 


775 


45 


28 


615 


10 


327 


775 


50* 


28 


615 


8 


400 


775 


61* 


30 


706 


12 


231 


890 


44 


30 


706 


11 


254 


890 


48 


30 


706 


10 


304 


890 


54 


30 


706 


8 


375 


890 


65 


30 


706 


7 


425 
141 


890 


74 


83 


1017 


11 


1300 


58 


m 


1017 


10 


155 


1300 


67 


36 


1017 


8 


192 


1300 


78 


36 


1017 


7 


210 


1300 


88 


40 


1256 


10 


141 


1600 


71 


40 


1256 


8 


174 


1600 


86 


40 


1256 


7 


189 


1600 


97 


40 


1256 


6 


213 


1600 


108 


40 


1256 


4 


250 


1600 


126 


4 s ? 


1385 


10 


135 


1760 


74* 


4->, 


1385 


8 


165 


1760 


91 


A?, 


1385 


7 


180 


1760 


102 


4", 


1385 


6 


210 


1760 


114 


42 


1385 


4 


240 


1760 


133 


49, 


1385 


y 


270 


1760 


137 


4'* 


1385 


3 


300 


1760 


145 


42 


1385 


tV 


321 


1760 


177 


42 


1385 


■ : fi 


363 


. 1760 


216 



USEFUL TABLES. 



?*i 


rt 


K3 


c< 


o 


*> 


W 


N 


Cr 


N 


CO 




00 


. 


vS 


\ 




2 i 


fO 


* 


<o 


so 


K 


CO 


CO 


=0 


CQ 


SO 


«i 


f\ 


- 


«1 




> i 


<r.. 


<o 


S8 


K. 


CT 


- 


m 


<o 


N 


rt 


N. 




\£> 


<r 


W 






Q 


o 


o 


o 












rl 


<N' 


«) 


rO 


T 


<« 






Q 








o 


O 


o 





o 








O 















}i 


N 


CO 


cr 





H 


■3* 




CO 





fc 


<j 


<o 











i«r 


-T 


T 


^r 


<o 


<o 


<0 


s 


<0 


so 


so 


N 


N 


93 


cr 





Q) 


X 
































w 


'- 


































s» 


^ 
































i- 


eo 


- 


f> 


w 


o 


NO 


o 


rO 


* 


■3- 


d 


CO 


* 


CO 


_ 




cO 


> E 





* 


>-n 





<^ 


iti 


CO 


o 


H 


•T 


^0 


N. 


cr 


o 


rl 


>N^ 






.pi 


S3 


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o 


- 


rt 


rO 


<o 


X) 


rv, 


<o 


<3- 


o 


d 


fO 


^ 




CO 


CH 


CO 


cr 


cr 


•<r 


cr 


cr 


cr 


<T 


o-> 


c- 


o 


o 


<i 


o 






wt""- 


























- 


- 


~ 


O 


z^i 


































"^3 

> 


;»c!l 






































































i ■ •* 






































J >« s 












o 











o 





o 


o 





o 





O 


CV 


iyj 




-5 * 








rt 


•0 




CO 

»0 


cr 


o 


<x 








(a 


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I 
































> 






' 






























o 

5 


r: J ! J" 




£% 


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to 


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CO 


cr- 


K. 


« 


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<o 


H 


5*, 


N 


<o 


«o 





K 


<*> 


cr- 


<o 





*o 


<i 


<o 


T 


fO 


K 




•Ji 


S9 


T 

so 


s3 


CO 

ss 


so 


IN 






so 
K 






o 

CO 


CO 


CO 


CO 




r £ * % ■* 4 






































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IS 






































j 








„ 
















o 











Q 







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00 


rj- 





— 


N 


eo 


^T 


k) 


VJ> 


K 


«D 


cr 





- 


1 "1 ! ! ! - 






- 


— 


si 


Pi 


N 


Csf 


rt 


M 


cv 


rj 


w 


n 


r0 


(0 


*.« 
































1 Jr'*" r p z 






















^ili££^ 


« 
































2^ 


H 


so 


to 


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K 


sO 


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fc 


d 


N 


_ 


N 


t 


fO 


*\ 


1 1 


i's 


m 


(O 


T 





rt 


H 





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cr 


cr 


eo 




£ j. 


- 


so 





T 


r\ 


o 


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CO 


o 


rt 


<r 


vO 


<o 


o 


U) C±T 


■I s * 


ol 


d 


flO 


m 


/o 


^r 


^r 


^ 


'T 


<o 


h 


lo 


b 


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so 




vn" 
































V 


































"5 





































































1 




o 


O 


o 




Q 










o 


o 







o 


o 






* u 


f< 


m 


<t 


fc 


SO 


K 


00 


<r 





- 


rt 


<f) 


<r 


<n 


^ 


I 


r -5 



































USEFUL TABIDS. 



The following is a very useful table and should be employed 
in Compressed Air distribution. The efficiency of many plants 
would be increased if the piping followed these proportions: 

Equation of Pipes.— It is frequently desired to know what number 
of pipes of a given size are equal in carrying capacity to one pipe of a larger 
size. At the same velocity of flow the volume delivered by two pipes of 
different sizes is proportional to the squares of their diameters; thus, one 
4-inch pipe will deliver the same volume as four 2-iuch pipes. With the same 
head, however, the velocity is less in the smaller pipe, and the volume de- 
livered varies about as the square root of the fifth power (i.e., as the fc.5 
power). The following table has been calculated on this basis. The figures 
opposite the intersection of any two sizes is the number of the smaller-sized 
pipes required to equal one of the larger. Thus, one 4-inch pipe is equal to 
5.7 2-inch pipes. 



c3 a 

5'" 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


12 


14 


16 


18 


20 


24 


2 


5.7 


1 






























3 


15.6 


2.8 


1 




























4 


32 


5.7 


2.1 


1 


























5 


55.9 


9.9 


3.6 


17 


1 
























6 


88.2 


15.6 


5 7 


2.8 


1.6 


1 






















7 


130 


22.9 


8 3 


4.1 


2.3 


1.5 


1 




















8 


181 


32 


11.1 


5.7 


3.2 


2.1 


1.4 


1 


















9 


243 


43. 


15.6 


76 


4.3 


2 8 


1.9 


1.3 


1 
















10 


316 


55.9 


20.3 


9.9 


5.7 


3.6 


2.4 


1.7 


1 3 


1 














11 


401 


70.9 


25.7 


12.5 


7.2 


4.6 


3.1 


2.2 


1.7 


1.3 














12 


499 


88.2 


32 


15.6 


8.9 


5.7 


3 8 


2.8 


2.1 


1.6 


1 












13 


609 


108 


39.1 


19 


10.9 


7.1 


4.7 


3.4 


2.5 


1.9 


1.2 












14 


733 


130 


47 


22.9 


13.1 


8.3 


5.7 


4.1 


3.0 


2 3 


1.5 


1 










15 


787 


154 


.55.9 


27.2 


15.6 


9.9 


6.7 


4.8 


3 6 


2 8 


1.7 


1.2 










16 




181 


65.7 


32 


18.3 


11.7 


7.9 


5.7 


4.2 


3.2 


2.1 


1.4 


1 








17 




213 


76.4 


37.2 


21.3 


13.5 


9.2 


6.6 


4.9 


3.8 


2.4 


1.6 


1.2 








18 




243 


88.2 


43 


24.6 


15.6 


10 6 


7.6 


5.7 


4.3 


2.8 


1.9 


1.3 


1 






19 




278 


101 


49.1 


28.1 


17.8 


12.1 


8.7 


6.5 


5 


3.2 


2.1 


1.5 


1.1 






20 




MIC 


115 


559 


32 


20.3 


13 8 


9.9 


7.4 


5.7 


3.6 


2.4 


1.7 


1.3 


1 




22 




401 


N6 


70 9 


40.6 


25.7 


17.5 


12.5 


9.3 


7.2 


4.6 


3.1 


2.2 


1.7 


1.3 




24 




109 


181 


88 2 


50.5 


32 


21 8 


15.6 


11.6 


8.9 


5.7 


3 8 


2.8 


2.1 


1.6 


1 


26 




609 


221 


108 


61.7 


39.1 


26.6 


19. 


14.2 


10.9 


7.1 


4.7 


3 4 


2.5 


1.9 


1.2 


28 




733 


266 


130 


74.2 


47 


32 


22.9 


17 1 


13.1 


8.3 


5.7 


4.1 


3 


2.3 


1.5 


30 




7S7 


316 


154 


S8.2 


55.9 


38 


27.2 




15.6 


9.9 


6.7 


4.8 


3.6 


2.8 


1.7 


36 






199 


243 


130 


88.2 


60 


43 f32 


24.6 


15.6 


10.6 


7.6 


5.7 


4.3 


2.8 


42 






733 


357 


205 


130 


88.2 


63.2|47 




1.9 


15 6 


11.2 


8.3 


6.4 


4.1 


48 








409 


286 


181 


123 


88.2162.7 


50.5 


32 


25.8 


15.6 


11.6 


8.9 


5.7 


54 








670 


383 


243 


105 


118 ]88.2 67.8 


43 


29.2 


20.9 


15.6 


12 


7.6 


60 








787 


409 


316 


215 


154 


115 


88.2 


55.9 


38 


27.2 


20.3 


15.6 


9.9 



USEFUL TABIDS 



213 



Used in the calculation of problems in Isothermal Compres- 
sion and .Expansion of Compressed Air. 







HYPERBOLIC 


LOGARITHMS. 






No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


1.01 


.0099 


1.45 


.3716 


1.89 


.6366 


2.33 


.8458 


2.77 


1.0188 


1.02 


.0198 


1.46 


.3784 


1.90 


.6419 


2.34 


.8502 


2.78 


1.0225 


1.03 


.0296 


1.47 


.3853 


1.91 


.6471 


2.35 


.8544 


2.79 


1.0260 


1.04 


.0392 


1.48 


.3920 


1.92 


.6523 


2.36 


.8587 


2.80 


1.0296 


1.05 


.0488 


1.49 


.3988 


1.93 


.6575 


2.37 


.8629 


2.81 


1.0332 


1.06 


.0583 


1.50 


.4055 


1.94 


.6627 


2.38 


.8671 


2.82 


1.0367 


1.07 


.0677 


1.51 


.4121 


1.95 


.6678 


2.39 


.8713 


2.83 


1.0403 


1.08 


.0770 


1.52 


.4187 


1.96 


.6729 


2.40 


.8755 


2.84 


1.0438 


1.09 


.0862 


1.53 


.4253 


1.97 


.6780 


2.41 


.8796 


2.85 


1.0473 


1.10 


.0953 


1.54 


.4318 


1.98 


.6831 


2.42 


.8838 


2.86 


1.0508 


1.11 


.1044 


1.55 


.4383 


1.99 


.6881 


2.43 


.8879 


2.87 


1.0543 


1.12 


.1133 


1.56 


.4447 


2.00 


.6931 


2.44 


.8920 


2.88 


1.0578 


1.13 


.1222 


1.57 


.4511 


2.01 


.6981 


2.45 


.8961 


2.89 


1.0613 


1.14 


.1310 


1.58 


.4574 


2.02 


.7031 


2.46 


.9002 


2.90 


1.0647 


1.15 


.1398 


1.59 


.4637 


2.03 


.7080 


2.47 


.9042 


2.91 


1.0682 


1.16 


.1484 


1.60 


.4700 


2.04 


.7129 


2.48 


.9083 


2.92 


1.0716 


1.17 


.1570 


1.61 


.4762 


2.05 


.7178 


2.49 


.9123 


2.93 


1.0750 


1.18 


.1655 


1.62 


.4824 


2.06 


.7227 


2.50 


.9163 


2.94 


1.0784 


1.19 


.1740 


1.63 


,4886 


2.07 


.7275 


2.51 


.9203 


2.95 


1.0813 


1.20 


.1823 


1.64 


.4947 


2.08 


.7324 


2.52 


.9243 


2.96 


1.0852 


1.21 


.1906 


1.65 


.5008 


2.09 


.7372 


2.53 


.9282 


2.97 


1.0886 


1.22 


.1988 


1.66 


.5068 


2.10 


.7419 


2.54 


.9322 


2.98 


1.0919 


1.23 


.2070 


1.67 


.5128 


2.11 


.7467 


2.55 


.9361 


2.99 


1.0953 


1.24 


.2151 


1.68 


.5188 


2.12 


.7514 


2.56 


.9400 


3.00 


1.0986 


1.25 


.2231 


1.69 


.5247 


2.13 


.7561 


2.57 


.9439 


3.01 


1.1019 


1.26 


.2311 


1.70 


.5306 


2.14 


.7608 


2.58 


.9478 


3.02 


1.1053 


1.27 


.2390 


1.71 


,5365 


2.15 


.7655 


2.59 


.9517 


3.03 


1.1086 


1.28 


.2469 


1.72 


.5423 


2.13 


.7701 


2.60 


.9555 


3.04 


1.1119 


1.29 


.2546 


1.73 


.5481 


2.17 


.7747 


2.61 


.9594 


3.05 


1.1151 


1.30 


.2624 


1.74 


.5539 


2.18 


.7793 


2.62 


.9632 


3.06 


1.1184 


1.31 


.2700 


1.75 


.5596 


2.19 


.7839 


2.63 


.9670 


3.07 


1.1217 


1.32 


.2776 


1.76 


.5653 


2.20 


.7885 


2.64 


.9708 


3.08 


1.1249 


1.33 


.2852 


1.77 


.5710 


2.2! 


.7930 


2.65 


.9746 


3.09 


1.1282 


1.34 


.2927 


1.78 


.5766 


2.22 


.7975 


2.66 


.9783 


3.10 


1.1314 


1.35 


.3001 


1.79 


.5822 


2.28 


.8020 


2.67 


.9821 


3.11 


1.1346 


1.36 


.3075 


1.80 


.5878 


2.24 


.8065 


2.68 


.9858 


3.12 


1.1378 


1.37 


.3148 


1.81 


.5933 


2.25 


.8109 


2.69 


.9895 


3.13 


1.1410 


1 tt 


.3221 


1.82 


.5988 


2.26 


.8154 


2.70 


.9933 


3.14 


1.1442 


1.33 


.3293 


1.83 


.6043 


2.27 


.8198 


2.71 


.9969 


3.15 


1.1474 


:ao 


.3365 


1.84 


.6098 


2.28 


.8242 


2.72 


1.0006 


3 16 


1.1506 


1.41 


.um 


1.85 


.6152 


2.29 


,8286 


2.73 


1.0043 


3.17 


1.1537 


1.42 


.3507 


1.86 


.<>206 


2.30 


.8329 


2.74 


1.0080 


3.18 


1.1569 


1.43 


.3577 


1.87 


.6259 


2.31 


.8372 


2.75 


1.0116 


3.19 


1.1600 


1.44 


.3646 


1.88 


.6313 


2.32 


• 8416 


2.76 


1.0152 


3.20 


1.1632 



214 



USEFUL TABLES. 
HYPERBOLTC LOGARITHMS. 



No.. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


3.21 


1.1663 


3.87 


1.3533 


4.53 


1.5107 


5.19 


1.6467 


5.85 


1.7664 


3.22 


1.1694 


3.88 


1.3558 


4.54 


1.5129 


5.20 


1.6487 


5.86 


1.7681 


3.23 


1.1725 


3.89 


1.3584 


4.55 


1.5151 


5.21 


1.6506 


5.87 


1.7699 


3.24 


1.1756"" 


3.90 


1.3610 


4.56 


1.5173 


5.22 


1.6525 


5.88 


1.7716 


3.25 


1.1787 


3.91 


1.3635 


4.57 


1.5195 


5.23 


1.6514 


5.89 


1.7733 


3.26 


1.1817 


3.92 


1.3661 


4.58 


1.5217 


5.24 


1.6563 


5.90 


1.7750 


3.27 


1.1848 


3.93 


1.3686 


4.59 


1.5239 


5.25 


1.6582 


5.91 


•1.7766 


3.28 


1.1878 


3.94 


1.3712 


4.60 


1.5261 


5.26 


1.6601 


5.92 


1.7783 


3.29 


1.1909 


3.95 


1.3737 


4.6i 


1.5282 


5.27 


1.6620 


5.93 


1.780C 


3.30 


1.1939 


3.96 


1.3762 


4.62 


1.5304 


5.28' 


1.6639 


5.94 


1.7817 


3.31 


1 1969 


3.97 


1.3788 


4.63 


1.5326 


5.29 


1.6658 


5.95 


j .7834 


3.32 


1.1999 


3.98 


1.3813 


4.64 


1.5347 


5.30 


1.6677 


5.96 


1.7851 


3.33 


1.2030 


3.99 


1.3838 


4.65 


1.5369 


5.31 


1.6696 


5.97 


1.7867 


3.34 


1.2060 


4.00 


1.3863 


4.66 


1.5390 


5.32 


1.6715 


5.98 


1.7884 


3.35 


1.2090 


4.01 


1.3888 


4.67 


1.5412 


5.33 


1.6734 


5.99 


1.7901 


3.36 


1.2119 


4.02 


1.3913 


4.68 


1.5433 


5.34 


1.6752 


6.00 


1.7918 


8.37 


1.2149 


4.03 


1.3938 


4.69 


1.5454 


5.35 


1.6771 


6.01 


1.7934 


3.38 


1.2179 


4.01 


1.3962 


4.70 


1.5476 


5.36 


1.6790 


6.02 


1.7951 


3.39 


1.2208 


4.05 


1.3987 


4.71 


1.5497 


5.37 


1.6808 


6.03 


1.7967 


3.40 


1.2238 


4.06 


1.4012 


4.72 


1.5518 


5.38 


1.6827 


6.04 


1.7984 


3.41 


1.2267 


4.07 


1.4036 


4.73 


1.5539 


5.39 


1.6845 


6.05 


1.8001 


3.42 


1.2296 


4.08 


1.4061 


4.74 


1.5560 


5.40 


1.6864 


6.06 


1.8017 


3.43 


1.2326 


4.09 


1.4085 


4.75 


1.5581 


5.41 


1.6882 


6.07 


1.8034 


3.44 


1 .2355 


4.10 


1.4110 


4.76 


1.5602 


5.42 


1.6901 


6.08 


1.8050 


3.45 


1.2384 


4.11 


1.4134 


4.77 


1.5623 


5.43 


1.6919 


6.09 


1.8066 


3.46 


1.2413 


4.12 


1.4159 


4.78 


1.5644 


5.44 


1.6938 


6.10 


1.8083 


3.47 


1.2442 


4.13 


1.4183 


4.79 


1.5665 


5.45 


1.6956 


6.11 


1.8099 


3.48 


1.2470 


4.14 


1.4207 


4.80 


1.5686 


5.46 


1.6974 


6.12 


1.8116 


3.49 


1.2499 


4.15 


1.4231 


4.81 


1.5707 


5.47 


1.6993 


6.13 


1.8132 


3.50 


1.2528 


4.16 


1.4255 


4.82 


1.5728 


5.48 


1.7011 


6.14 


1.8148 


3.51 


1.2556 


4.17 


1.4279 


4.83 


1.5748 


5.49 


1.7029 


6.15 


1.8165 


3.52 


1.2585 


4.18 


1.4303 


4.84 


1 .5769 


5.50 


1.7047 


6.16 


1.8181 


3.53 


1.2613 


4.19 


1.4327 


4.85 


1.5790 


5.51 


1.7066 


6.17 


1.8197 


3.54 


1.2641 


4.20 


1.4351 


4.86 


1.5810 


5.52 


1.7084 


6.18 


1.8213 


3.55 


1.8669 


4.21 


1.4375 


4.87 


1.5831 


5.53 


1.7102 


6.19 


1.8229 


3.56 


1.2698 


4.22 


1.4398 


4.88 


1.5851 


5.54 


1.7120 


6.20 


1.8245 


3.57 


1.2726 


4.23 


1 .4422 


4.89 


1.5872 


5.55 


1.7138 


6.21 


1.8262 


3.58 


1.2754 


4.24 


1.4446 


4.90 


1.5892 


5.56 


1.7156 


6.22 


J. 8278 


3.59 


1.2782 


4.25 


1.4469 


4.91 


1.5913 


5.57 


1.7174 


6.23 


1.8294 


3.60 


1.2809 


4.26 


1.4493 


4.92 


1.5933 


5.58 


1.7192 


6.24 


1.8310 


3.61 


1.2837 


4.27 


1.4516 


4.93 


1.5953 


5.59 


1.7210 


6.25 


1.8326 


3.62 


1.2865 


4.28 


1.4540 


4.94 


1.5974 


5.60 


1.7228 


6.26 


1.8342 


3.63 


1.2892 


4.29 


1.4563 


4.95 


1.5994 


5.61 


1.7246 


6.27 


1.8358 


3.64 


1.2920 


4.30 


1.4586 


4.96 


1.6014 


5.62 


1.7263 


6.28 


1.8374 


3.65 


1.2947 


4.31 


1.4609 


4.97 


1.6034 


5.63 


1.7281 


6.29 


1.8390 


3.66 


1.2975 


4.32 


1.4633 


4.98 


1.6054 


5.64 


1.7299 


6.30 


1.8405 


3.67 


1.3002 


4.33 


1 .4656 


4.99 


1.6074 


5.65 


1.7317 


6.31 


1.8421 


3.68 


1.3029 


4.34 


1.4679 


5.00 


1.6094 


5.66 


1.7334 


6.32 


1.8437 


3.69 


1.3056 


4.35 


1.4702 


5.01 


1.6114 


5.67 


1.7352 


6.33 


1.8453 


3.70 


1.3083 


4.36 


1.4725 


5.02 


1.6134 


5.68 


1.7370 


6.34 


1.8469 


3.71 


1.3110 


4.37 


1.4748 


5.03 


1.6154 


5.69 


1.7387 


6.35 


1.8485 


3.72 


1.3137 


4.38 


1.4770 


5.04 


1.6174 


5.70 


1.7405 


6.36 


1.8500 


3.73 


1.3164 


4.39 


1.4793 


5.05 


1.6194 


5.71 


1.7422 


6.37 


1.8516 


3.74 


1.3191 


4.40 


1.4816 


5.06 


1.6214 


5.72 


1 .7440 


6.38 


1.8532 


3.75 


1.3218 


4.41 


1.4839 


5.07 


1.6233 


5.73 


1.7457 


6.39 


1.8517 


3.76 


1.3244 


4.42 


1.4861 


5.08 


1.6253 


5.74 


1.7475 


6.40 


1.8563 


3.77 


1.3271 


4.43 


1.4884 


5.09 


1.6273 


5.75 


1.7492 


6.41 


1.8579 


3.78 


1.3297 


4.44 


1.4907 


5.10 


1.6292 


5.76 


1.7509 


6.42 


1.8594 


3.79 


1.3324 


4.45 


1.4929. 


5.11 


1.6312 


5.77 


1.7527 


6.43 


1.8610 


3.80 


1.3350 


4.46 


1.4951 


5.12 


1.6332 


5.78 


1.7544 


6.44 


1.8625 


3.81 


1.3376 


4.47 


1.4974 


5.13 


1.6351 


5.79 


1.7561 


6.45 


1.8641 


3.82 


1.3403 


4.48 


1.4996 


5.14 


1.6371 


5.80 


1.7579 


6.46 


1.8056 


3.83 


1.3429 


4.49 


1.5019 


5.15 


1 .6390 


5,81 


-1.7596 


6.47 


1.8672 


3.84 


1.3455 


4.50 


1.5041 


5.16 


1.6409 


5.82 


1.7613 


6.48 


1.8687 


3.85 


1.3481 


4.51 


1.5063 


5.17 


1.6429 


5.83 


1 .76% 


6.49 


1.8703 


3.86 


1.3507 


4.52 


1.5085 


5.18 


1.6448 


5.84 


1.7647 1 


6.50 


1.8718 



USEFUL TABLES. 



215 



Volume, wensity, and Pressure of Air at Various 

Temperatures. (D.K.Clark.) 





Volume at Atinos. 




Pressure at Constant 




Pressure. 


Density, lbs. 


Volume. 






per Cubic Foot at 
Atmos. Pressure. 






Fahr. 












Cubic Feet 


Compara- 




Lbs. per 


Compara- 
tive Pres. 




in 1 lb. 


tive Vol. 




' Sq. In. 





11.583 


.881 


.086331 


12.96 


.881 


32 


12.387 


.943 


.080728 


13.86 


.943 


40 


12.586 


.958 


.079439 


14.08 


.958 


50 


12.840 


.977 


.077884 


14.36 


.977 


62 


13.141 


1.000 


.076097 


14.70 


1.000 


70 


13.342 


1.015 


.074950 


14.92 


1.015 


80 


13.593 


1.Q34 
1.054 


.073565 


15.21 


1.034 


90 


13.845 


.072230 


15.49 


1.054 


100 


14.096 


1.073 


.070942 


15.77 


1.073 


no 


14.344 


1.092 


.069721 


16.05 


1.092 


120 


14.592 


1.111 


.06^500 


16.33 


1.111 


130 


14.846 


1.130 


.067361 


16.61 


1.130 


140 


15.100 


1.149 


.066221 


16.89 


1.149 


150 


15.351 


1.168 


.065155 


17.19 


1.168 


160 


15.603 


1.187 


.064088 


17.50 


1.187 


170 


15.854 


1.206 


.063089 


17.76 


1.206 


180 


16.106 


1.226 


.062090 


18.02 


1.226 


200 


16.606 


1.264 


.060210 


18.58 


1.264 


210 


16.860 


1.283 


.059313 


18.86 


1.283 


212 


16.910 


1.287 


.059135 


18.92 


1.287 



2l6 



USEFUL TABLES, 



Volumes, mean Pressures per Stroke, Temperatures, etc.. 
in the Operation of Air-compression from 1 Atmosphere 

and 60° Fahr, (F. Richards, Am. Mack., March 30, 1893.) 



















t- _• i t. 






6 

3 

| 

9- 
i 


CO 

w 
O 

s 


|1 


< 

* O 


to ft 

a, jj c 


m 


o 

3 

<i 
•si 

o 

ft 

3 


6 

3 

3 

9 
ft 
i 

3 


CO 

u 

ft 
O 

a 


- a, 
1% 

So 


< 

■si 

V 


0/ . 


0> 

p a 

3 — "O 

£ i>'o 

«5-^ 


c 

3 

O O 
o 

ft 

§ 


«5 




©^ 


o 


JJCQ 


0)73 




cd 




0*> 


o 


Vrn 


0)02 


35 


< 


> * 


5> 


§ 


H 


o 


< 


> a 


> 


£T 


s 


1 


S 


3 


4 


5 


6 


7 


1 


2 


3 


4 


5 


6 


7 





1 


1 


1 








60° 


80 


6. 442. 1552 


.267 


27.38 


36.64 


"432 


1 


J. 068 


.9363 


.95 


.96 


.975 


71 


85' 6.182 


.1474 


2566 


28.16 


37.94 


447 


2 


1.136 


.8803 


.91 


1.87 


.1.91 


80.4 


90! 7.122 


.1404 


.248 


28.89 


39.18 


459 


3 


1.204 


.8305 


.876 


2.72 


2 8 


88.9 


95 ! 7.462 


.134 


.24 


29.57 


40.4 


472 


4 


1.272 


.7861 


.84 


3.53 


H 67 


98 


100 1 7.802' 1281 


.232 


30.21 


41.6 


485 


5 


1.34 


.7462 


.81 


4.3 


4 5 


106 


1051 8.1421 1228 


2254 


30.81 


42.78 


496 


10 


1 68 


.5952 


.69 


7.62 


8.27 


145 


110 8 483 .1178 


.2189 


31.39 


43.91 


507 


15 


2.02 


.495 


.606 


10.33 


11.51 


178 


1151 8 823' .1133 


.2129 


31.98 


44.98 


518 


SO 


2.36 


.4237 


.543 


12.62 


14.4 


207 


120, 9.163' 1091 


.2073 


32.54 


46.04 


529 


25 


2.7 


.3703 


.494 


14.59 


17.01 


234 


125 9. 503.. 1052 


.2020 


33.07 


47.06 


540 


30 


3!oi 


3289 


.4538 


16.34 


19.4 


252 


130 9.843 .1015 


.1969 


33.57 


48.1 


550 


35 


3.3S1 


.2957 


.42 


17.92 


21.6 


281 


135 10.183' 0981 


.1922 


34.05 


49.1 


560 


40 


3.721 


.2687 


393 


19.32 


23 66 


302 


140 10.5?3'.095 


.1878 


34.57 


50.02 


570 


45 


1.061 


.2462 


.37 


20.57 


*5.59 


321 


145 10.864 .0921 


.1837 


35.09 


51. 


580 


MJ 


4.401 


.2272 


.35 


21.69 


27.39 


339 


150 11.204 .0892 


.1796 


35.48 


51.89 


589 


r>r> 


4.741 


.2109 


331 


22.76 


29.11 


357 


160 11.88 


.0841 


.1722 


36.29 


53.65 


607 


fiO 


5.081 


.1968 


.3144 


23 . 78 


30 75 


375 


170 12.56 


0796 


.1657 


37.2 


55.39 


624 


65 


0.423 


.1844 


.301 


24.75 


32 32 


389 


180 13 24 


0755 


.1595 


37.96 


57.01 


640 


70 


5.762 


.1735 


288 


25 67 


33.83 


405 


190 13.92 


.0718 


.154 


38.68 


58.57 


657 


?S 


6.102 


.1639 


.276 


26.55 


35.2? 


420 


200 14.6 


.0685 


.149 


39.42 


60.14 


672 



USEFUL TABLES. 



Mean and Terminal Pressures of Compressed AJr used 
Expansively for Gauge-pressares from 60 to 100 lbs. 

(Frank Richards, Am. Mack, April 13, 5893.) 



Initial 
Pres- 


60. 


70. 


80. 


90. 


100 


sure. 












ojb 


SU§ 


.Si 5 


B . 2 


Bc.3 


« 1 
* u S 


* s 


3 ". *■ 


*3 a) 


0) 


*3 © 

.5.- % 


O 3 


£<% 


£<% 




%<% 


£^£ 


l<l 


4T-5 " 


WJ 


m 


&o 


a 


b* a 


ft 


£ fe 


a 


£ S. 


39 04 


£ p, 
J4.91 


ft 


£ ft 


.25 


23.6 


10 65 


28.74 


12.07 


33.89 


13.49 


44.19 


1.33 


.30 


28.9 


13.77 


34.75 


6 


40 61 


2.44 


46 46 


4.27 


53.32 


6 11 


l A 


32.13 


,96 


38.41 


3.09 


44.69 


5 22 


50.98 


7 35 


57 26 


9 48 


.35 


33.66 


2.33 


40. T5 


4.38 


46.64 


6.66 


53.13 


8 95 


59 62 


11.23 


& 


35.85 


3.85 


42 63 


6.36 


49.41 


7.88 


56 2 


11.39 


62 98 


13.559 


37.93 


5.64 


44.99 


8.39 


52.05 


11.14 


59.11 


13.88 


66 16 


16.64 


,45 


41.75 


10.71 


49.31 


12.61 


56.9 


15.86 


64 45 


19.11 


72.02 


22.36 


.50 


45.14 


13.26 


53.16 


17 


61.18 


20 81 


69.19 


24 56 


77.21 


2S.33 


,60 


50.75 


21.53 


59.51 


26.4 


68.28 


31 27 


77.05 


36.14 


85.82 


41 01 


% 


51.92 


23.69 


60.84 


28.85 


69.76 


34.01 


78.69 


39.16 


87.61 


44.32 


ft 


53.67 


27.94 


62 83 


33.03 


71.99 


38.68 


81 14 


44 33 


90.32 


49 97 


54.93 


30.39 


64 25 


36 44 


73.57 


42.49 


82 9 


48.54 


92.22 


54.59 


.75 


56.52 


35.01 


66.05 


41.68 


75.59 


48.35 


85.12 


55.02 


94.66 


61 69 


.80 


57.79 


30.78 


67.5 


47.08 


77.2 


54.38 


86.91 


61.69 


96.61 


68.99 


% 


59.15 


47.14 


69.03 


55.43 


78.92 


63.81 


88.81 


72. 


9S.7 


80 28 


.90 


59.46 


49.65 


69.38 


58.27 


79 31 


66 89 


89.24 


75.52 


99.17 


87 82 



The pressures in the table are all gauge-pressures except those in italics 
which are absolute pressures (above a vacuum). 



218 



USEFUL TABIDS. 



R 


K 


PV, 

p, 


R 


t 


PV» 

p, 


2 


. o5 


/99s 


5 


• ^ 


.5218 


1 8 


.055 


. 5.I 6 I 


4.4 4 


. z zs 


. 5^08 


I 6 


. 06* 


. 2ZS8 


4. 


. z 5 


. 5^65 


1 5 


. 6 66 


. IhjZ 


3. 6 3 


. 2,7 S 


. 6*3o5 


1 4 


. 07/ 


. 25^ 


3.3 3 


. 3 


. 6"6i 5 


13.33 


. 0/5 


. Z6cj 


3 


.333 


.6-^3 


1 3 


• 07/ 


. ^74^ 


2.86 


. 3 S 


. 7.7. 


1 X 


. o83 


. 2(|.0^ 


Z6 6 


. 3 7 S 


,/44 


1 1 


.091 


. 3o8cj 


Z- So 


•4 


.^6et4 


1 


. 1 


. 33e>3 


Z.ZZ 


. 4 5" 


. 8095 


q 


.III 


. 3 55^ 


2. 


♦ 5 


. 8465 


8 


. ins 


. sa^ 


1. SZ 


, 5 s 


. 8/86 


7 


.143 


. 4AI 


A. 6 6 


. 6 


. 9066 


6.6 6 


• / 5" 


.434/ 


1.6 


. 6a5 


• 9 ' 8 7 


6 


. !66 


. 4653 


1.5-4 


. 6 5* 


.QJLCJ2 


S. 7 i 


• i 7 5- 


.^807 


1.4 8 


, 6 j S 


. C}4 o5 


J T^U 


•€. of Mean Absolute Pressures 

l/anows Decrees of IsotkeTmaL Expansion — » 




_f.r 


P, i«, rtv«, 

P», IS tf» 

R_ ,s 4 

C 3 W» 

± inel.< 

B, 


— In this Table 

Absolute. Pressure. o»V whick. Sticuw. ev\T"er.S M\e. C 
e. corveipondma Mian Absolut*. Pressure. , 
e. Hate of E*p* wJ »' OM -, '"•"•• Hve. /Ratto «f Hit VoWd v 

o\e.T , I'weW.'n^ CUo.ra.wc, U U\i Volunn* of Lw«- SVt»w, 
ftttS Hit point- of Cu.r.off, ifc.fU Ratio of Hie. h>Ul Vol 
v ft. rUt Voho.1 Volume of Cvli'i*cUv <xr U»«. End of H10. S 


yli'wder, 









USEFUL TABLES. 



219 



Nowi 1 v\o.l 

lv»cK»6 — 


Actw.ev.1 


N»Wll'M«l 
Wciabl- 

— Utf 


Number »f Tkrea^j 
of Scrtw 


a. 


* * 


«a. 2 z 


14 


*•! 


2.- J 


Z- 8 z. 


1 4 


*'k 


*•* 


3- 1 3 


1 4 


*•! 


3 


3- ^ 5" 


1 4 


3. 


3.J; 


4-16 


I 4 


*•* 


A- 4 


4 4$ 


1 4 


3-5 


3-1 


4/8 


J 4 


»•* 


4 


5. 5*6 


I 4 


4 


4-4 


6. 


1 4 


4-k 


4£ 


<£. 3 6 


I 4 


4-s 


4-.* 


/.7 3 


1 4 


4-J 


5" 


7io 


1 H 


(5" 


54 


g.2 


\H 


*fc 


5.± 


*■ 62, 


1 4 


*J 


6 


I . 4 6 


1 4 


** 


*f 


M- 5-8 


1 M 


*f 


7 


12.34 


1 4 


74 


7% 


J 3. s-s 


i M 


M 


8 


1 5- A 1 


u4 


8.* 


|.f 


/ 6 . e^ 


II.. £ 


••f 


°l 


17.^0 


M-i 


vf 


1 


A 1 • «J 


' '£ 


1 6. ? 

• 


I 1 


2 67^ 


Mi 


M'f 


1 2. 


3 35" 


M-i 


14 £ 


• 3 


33.7 8 


l|£ 


« ^ i 


J 4 


42o2, 


« ' i 


.4 i 


» 5" 


A 7 6 6 


1 »•£ 


Ui 


1 6 


St*/ 


»' k 


fc LiSf «f Well CqJl'wa. 


- 



USEFUL TABLES. 



. Bwtt -Welded 


Nom.'wat 


Actual 

. — lv\fct\t6 . _ 




— Lbs — 


N«*wb«y «(TlvY««<l» 
of ScYtVV 


8 


. 4 


.066 


. 2.4 


*7 


4 


. $•*■ 


• 8 8 


• 4a. 


1 8 


3 
8 


• V 


••1' 


. 5-6 


1 e 


J 


• 84 


• I a\ 


. 8* 


1 * 


3 
2f 


J. ©S - 


• l l 3 


lix 


1 * 


1 


I. 31 


> 1 3 4 


1C7 


' • i 


1 I 


1-66 


. I 4 


i.ji 


" £ 


— - Lap- Wcl4ed — — - 


NtMl'-MAl 

twSi'da. 


ActwoJ ' 

O i A vucfa f 


TVcKnets 


N»iwi*m*I 

[>»t Fo.h 
— L>4 


|»«.t IhcK 
of Screw 


»i 


l.<? 


.14 5 


2.6 8 


1 l.£ 


Z 


2.3/ 


. / 5-4 


3. 6» 


I »£ 


2. 1 


2 8? 


• iel 


S. 7 * 


$ 


3 


d. r 


.117 


7.3-4 


8 


5 i 


4 


•2*6 


<} 


8 


4 


4-5* 


.43/ 


1 0.66 


8 


A i 


s- 


. m; 


ia.34 


3 


S 


S.& 


.i5-q 


'1450 


8 


6 


6.62. 


. a. 6 


\S.76 


8 


7 


? 6*. 


• 3« 1 


i.3 2.7 


8 


8 


8.62. 


.jai 


as / a 


a 


9 


cj. «8 


• *44 


3 3. 7 * 


a 


/ 


I 075" 


• $66 


4o 


8 


i 1 


1 1. 75- 


• 375* 


45 


8 


> i 


12.7* 


.3^5 


4Q 


8 


i 3 


14 


• 37^ 


54 


8 


1 H 


IS 


• 37* 


S8 


» 


1$ 


16 


.3 7 5- 


6X 


8 


— List of Sffcawv, A»r «\h«i Ware/ P.>*S . 


- 



INDEX. 



PAGE 

A ir Compressors— General Remarks 81 

Air Engines 38 

Air Engines, Exhaust Temperatures and Reheating 50 

Air Receivers 182 

Available Work at Complete Expansion, Curve of. 30 

Available Work at Full Expansion, Table of. 31 

Blacksmith Tools 186 

Capacity of Compressors 84 

Calculation of H. P. of Water, Table of 207 

Circumferences and Areas of Circles 191 

Column Mountings 180 

Compressed Air, General Principles 3 

COMPRESSORS— 

Combined Duplex Steam Actuated and Shaft-driven Com- 
pressors, Class G 105 

Compound Corliss Actuated Compressors, Class J 110 

Direct Acting Steam Actuated Duplex Compressors, Light 

Duty, Class L 119 

Duplex Steam Actuated Compressors, Class A 86 

Duplex Shaft-driven Compressors, Class D 95 

Duplex Tandem Sectional Shaft-driven Compressors, Class E. 99 

Light Duty Compressor or Vacuum Pump, Class K 117 

Single Steam Compressors, Class B 91 

Single Steam Actuated Compressors, Self-contained Type, 

Class C 93 

Single Shaft-driven Compressors, Class F 102 

Single Corliss Actuated Compressors, Class 1 113 

Steam Actuated Vertical Compressors, Class H 108 

Steam Actuated Single Air Compressors, Class M 121 

Consumption of Air 40 

Consumption of Air, Single Cylinder Automatic Engines 41 

Consumption of Air, Compound Automatic Engines 42 

Consumption of Air, Single Cylinder Corliss Engines 43 

Consumption of Air, Compound Corliss Engines 44 

Consumption of Air, Corliss Compound Pneumatic Motors, Table 

of 51 

Consumption of Air for pumps 61 

Consumption of Air, Rock Drills 85 

Decimals of a Foot per Each Sixty-fourth of an Inch 202 

Decimals of an Inch for Each Sixty-fourth 206 

Difference of Level in Use of Compressed Air 35 

Difference of Level in Use of Compressed Air, Table of 37 

Equation of Pipes 212 

Expansion of Air 45 



INDEX. 

PAGE 

Fifth Roots and Fifth Powers 194 

General Hints 178 

Hyperbolic logarithms 213 

Indicated Horse Power to Compress Air 56 

Indicated Horse Power to Compress Air, Curve for 57 

Loss of Pressure in Pipes ". 21 

Loss of Pressure through Bends 33 

Loss of Pressure through Bends, Table of 34 

Loss of Head in Pipes! by Friction 208 

Lubricators and Lubricants 187 

Mean and Terminal Pressures of Compressed Air 217 

Mean Absolute Pressures Tor Various Degrees of Isothermal 

Expansion, Table of 218 

Mean Effective Pressures, Curve of 58 

Pneumatic Governors 127 

Pneumatic Hoist 52 

Pneumatic Locomotive 70 

Pneumatic Plant at Grass Valley 134 

Pneumatic Torpedo Plant at Presidio, S. F 140 

Power Transmission by Compressed Air 71 

Pressure in Vertical Pipes 59 

Quantity of Air Compressed per Indicated Horse Power 53 

Quantity of Air Compressed per Indicated Horse Power, Curve 

for 54 

Reheater 48 

Refrigeration by Compressed Air 63 

Rix Patent Hose Couplings 186 

ROCK DRILLS— 

Rock Drills 158 

Rock Drills, Rix, Table of 170 

Roak Drills, Giant, Table of 171 

Rock Drills, Plug and Feather 176 

Sheet Iron Hydraulic Pipe, Table of 210 

Squares, Cubes, and Reciprocals 195 

Tripod Mountings 165 

Temperatures, Centigrade, and Fahrenheit 200 

Volume, Density, and Pressure of Air at Various Temperatures. 215 

Volumes, Mean Pressure per Stroke, Temperatures 216 

Well Casing, List of 219 

Wrought Iron Pipe, List of 220 






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